In this paper, a function projective synchronization scheme is developed to investigate the function projective synchronization between the discrete-time driven chaotic system and the discrete-time response chaotic sy...In this paper, a function projective synchronization scheme is developed to investigate the function projective synchronization between the discrete-time driven chaotic system and the discrete-time response chaotic system. With the aid of symbolic-numeric computation, we use the scheme to study the function projective synchronization between 2D Lorenz discrete-time system and Hdnon discrete-time system, as well as that between 3D discrete-time hyperchaotic system and Henon-like map via three scalar controllers, respectively. Moreover numerical simulations are used to verify the effectiveness of the proposed scheme.展开更多
This paper presents a hybrid symbolic-numeric algorithm to compute ranking functions for establishing the termination of loop programs with polynomial guards and polynomial assignments.The authors first transform the ...This paper presents a hybrid symbolic-numeric algorithm to compute ranking functions for establishing the termination of loop programs with polynomial guards and polynomial assignments.The authors first transform the problem into a parameterized polynomial optimization problem,and obtain a numerical ranking function using polynomial sum-of-squares relaxation via semidefinite programming(SDP).A rational vector recovery algorithm is deployed to recover a rational polynomial from the numerical ranking function,and some symbolic computation techniques are used to certify that this polynomial is an exact ranking function of the loop programs.At last,the authors demonstrate on some polynomial loop programs from the literature that our algorithm successfully yields nonlinear ranking functions with rational coefficients.展开更多
Numerical approximate computations can solve large and complex problems fast.They have the advantage of high efficiency.However they only give approximate results,whereas we need exact results in some fields.There is ...Numerical approximate computations can solve large and complex problems fast.They have the advantage of high efficiency.However they only give approximate results,whereas we need exact results in some fields.There is a gap between approximate computations and exact results. In this paper,we build a bridge by which exact results can be obtained by numerical approximate computations.展开更多
In some fields such as Mathematics Mechanization, automated reasoning and Trustworthy Computing, etc., exact results are needed. Symbolic computations are used to obtain the exact results. Symbolic computations are of...In some fields such as Mathematics Mechanization, automated reasoning and Trustworthy Computing, etc., exact results are needed. Symbolic computations are used to obtain the exact results. Symbolic computations are of high complexity. In order to improve the situation, exact interpolating methods are often proposed for the exact results and approximate interpolating methods for the ap- proximate ones. In this paper, the authors study how to obtain exact interpolation polynomial with rational coefficients by approximate interpolating methods.展开更多
基金National Natural Science Foundation of China under Grant No.10735030Shanghai Leading Academic Discipline Project under Grant No.B412+3 种基金Natural Science Foundation of Zhejiang Province of China under Grant No.Y604056the Doctoral Foundation of Ningbo City under Grant No.2005A61030the Program for Changjiang Scholars and Innovative Research Team in Universities under Grant No.IRT0734K.C.Wong Magna Fund in Ningbo University
文摘In this paper, a function projective synchronization scheme is developed to investigate the function projective synchronization between the discrete-time driven chaotic system and the discrete-time response chaotic system. With the aid of symbolic-numeric computation, we use the scheme to study the function projective synchronization between 2D Lorenz discrete-time system and Hdnon discrete-time system, as well as that between 3D discrete-time hyperchaotic system and Henon-like map via three scalar controllers, respectively. Moreover numerical simulations are used to verify the effectiveness of the proposed scheme.
基金supported in part by the National Natural Science Foundation of China under Grant Nos.10901055,61021004,91118007by NKBRPC 2011CB302802,2011CB70690by the Fundamental Research Funds for the Central Universities under Grant No.78210043
文摘This paper presents a hybrid symbolic-numeric algorithm to compute ranking functions for establishing the termination of loop programs with polynomial guards and polynomial assignments.The authors first transform the problem into a parameterized polynomial optimization problem,and obtain a numerical ranking function using polynomial sum-of-squares relaxation via semidefinite programming(SDP).A rational vector recovery algorithm is deployed to recover a rational polynomial from the numerical ranking function,and some symbolic computation techniques are used to certify that this polynomial is an exact ranking function of the loop programs.At last,the authors demonstrate on some polynomial loop programs from the literature that our algorithm successfully yields nonlinear ranking functions with rational coefficients.
基金This work was partially supported by China 973 Project (Grant No.NKBRPC-2004CB318003)the Knowledge Innovation Program of the Chinese Academy of Sciences (Grant No.KJCX2-YW-S02).
文摘Numerical approximate computations can solve large and complex problems fast.They have the advantage of high efficiency.However they only give approximate results,whereas we need exact results in some fields.There is a gap between approximate computations and exact results. In this paper,we build a bridge by which exact results can be obtained by numerical approximate computations.
基金supported by China 973 Frogram 2011CB302402the Knowledge Innovation Program of the Chinese Academy of Sciences(KJCX2-YW-S02)+1 种基金the National Natural Science Foundation of China(10771205)the West Light Foundation of the Chinese Academy of Sciences
文摘In some fields such as Mathematics Mechanization, automated reasoning and Trustworthy Computing, etc., exact results are needed. Symbolic computations are used to obtain the exact results. Symbolic computations are of high complexity. In order to improve the situation, exact interpolating methods are often proposed for the exact results and approximate interpolating methods for the ap- proximate ones. In this paper, the authors study how to obtain exact interpolation polynomial with rational coefficients by approximate interpolating methods.
