This paper unfolds and reviews the theory of abstract algebra, field extensions and discusses various kinds of field extensions. Field extensions are said to be algebraic or transcendental. We pay much attention to al...This paper unfolds and reviews the theory of abstract algebra, field extensions and discusses various kinds of field extensions. Field extensions are said to be algebraic or transcendental. We pay much attention to algebraic extensions. Finally, we construct finite extensions of Q and finite extensions of the function field over finite field F<sub>p </sub>using the notion of field completion, analogous to field extensions. With the study of field extensions, considering any polynomial with coefficients in the field, we can find the roots of the polynomial, and with the notion of algebraically closed fields, we have one field, F, where we can find the roots of any polynomial with coefficients in F.展开更多
We consider an integrable three-dimensional system of ordinary differential equations introduced by S. V. Kovalevskaya in a letter to G. Mittag- Leffler. We prove its isomorphism with the three-dimensional Euler top, ...We consider an integrable three-dimensional system of ordinary differential equations introduced by S. V. Kovalevskaya in a letter to G. Mittag- Leffler. We prove its isomorphism with the three-dimensional Euler top, and propose two integrable discretizations for it. Then we present an integrable generalization of the Kovalevskaya system, and study the problem of integrable discretization for this generalized system.展开更多
Hadamard synergic control is a new kind of control problem which is achieved via a composite strategy of the state feedback control and the direct regulation of the part of connection coefficients of system state vari...Hadamard synergic control is a new kind of control problem which is achieved via a composite strategy of the state feedback control and the direct regulation of the part of connection coefficients of system state variables. Such a control is actually used very often in the practical areas. In this paper, we discuss Hadamard synergic stabilization problem for a class of dynamical networks. We analyze three cases: 1) Synergic stabilization problem for the general twonodenetwork. 2) Synergic stabilization problem for a special kind of networks. 3) Synergic stabilization problem for special kind of networks with communication timedelays. The mechanism of the synergic action between two control strategies: feedback control and the connection coefficients regulations are presented.展开更多
In this paper, we introduce a polynomial sequence in K[x], in which two neighbor polynomials satisfy a wonderful property. Using that,we give partial answer of an open problem： ifφ（x, y, z） = （f（x, y）, g（x, y...In this paper, we introduce a polynomial sequence in K[x], in which two neighbor polynomials satisfy a wonderful property. Using that,we give partial answer of an open problem： ifφ（x, y, z） = （f（x, y）, g（x, y, z）, z）, which sends every linear coordinate to a coordinate, then φ is an automorphism of K[x, y, z]. As a byproduct, we give an easy proof of the well-known Jung＇s Theorem.展开更多
The third order explicit autonomous differential equations named as jerk equations represent an interesting subclass of dynamical systems that can exhibit many major features of the regular and chaotic motion. In this...The third order explicit autonomous differential equations named as jerk equations represent an interesting subclass of dynamical systems that can exhibit many major features of the regular and chaotic motion. In this paper, we show that an algebraically simple system, the Genesio system can be recast into a jerky dynamics and its jerk equation can be derived from one-dimensional Newtonian equation. We also investigate the global dynamical properties of the corresponding jerk system.展开更多
This paper is concerned with the numerical dissipativity of multistep Runge-Kutta methods for nonlinear neutral delay-integro-differential equations.We investigate the dissipativity properties of-algebraically stable ...This paper is concerned with the numerical dissipativity of multistep Runge-Kutta methods for nonlinear neutral delay-integro-differential equations.We investigate the dissipativity properties of-algebraically stable multistep Runge-Kutta methods with constrained grid.The finite-dimensional and infinite-dimensional dissipativity results of-algebraically stable multistep Runge-Kutta methods are obtained.展开更多
This paper is concerned with the numerical dissipativity of multistep Runge-Kutta methods for nonlinear Volterra delay-integro-differential equations. We investigate the dissipativity properties of （k, l）- algebraic...This paper is concerned with the numerical dissipativity of multistep Runge-Kutta methods for nonlinear Volterra delay-integro-differential equations. We investigate the dissipativity properties of （k, l）- algebraically stable multistep Runge-Kutta methods with constrained grid and an uniform grid. The finite- dimensional and infinite-dimensional dissipativity results of （k, /）-algebraically stable Runge-Kutta methods are obtained.展开更多
文摘This paper unfolds and reviews the theory of abstract algebra, field extensions and discusses various kinds of field extensions. Field extensions are said to be algebraic or transcendental. We pay much attention to algebraic extensions. Finally, we construct finite extensions of Q and finite extensions of the function field over finite field F<sub>p </sub>using the notion of field completion, analogous to field extensions. With the study of field extensions, considering any polynomial with coefficients in the field, we can find the roots of the polynomial, and with the notion of algebraically closed fields, we have one field, F, where we can find the roots of any polynomial with coefficients in F.
文摘We consider an integrable three-dimensional system of ordinary differential equations introduced by S. V. Kovalevskaya in a letter to G. Mittag- Leffler. We prove its isomorphism with the three-dimensional Euler top, and propose two integrable discretizations for it. Then we present an integrable generalization of the Kovalevskaya system, and study the problem of integrable discretization for this generalized system.
文摘Hadamard synergic control is a new kind of control problem which is achieved via a composite strategy of the state feedback control and the direct regulation of the part of connection coefficients of system state variables. Such a control is actually used very often in the practical areas. In this paper, we discuss Hadamard synergic stabilization problem for a class of dynamical networks. We analyze three cases: 1) Synergic stabilization problem for the general twonodenetwork. 2) Synergic stabilization problem for a special kind of networks. 3) Synergic stabilization problem for special kind of networks with communication timedelays. The mechanism of the synergic action between two control strategies: feedback control and the connection coefficients regulations are presented.
文摘In this paper, we introduce a polynomial sequence in K[x], in which two neighbor polynomials satisfy a wonderful property. Using that,we give partial answer of an open problem： ifφ（x, y, z） = （f（x, y）, g（x, y, z）, z）, which sends every linear coordinate to a coordinate, then φ is an automorphism of K[x, y, z]. As a byproduct, we give an easy proof of the well-known Jung＇s Theorem.
文摘The third order explicit autonomous differential equations named as jerk equations represent an interesting subclass of dynamical systems that can exhibit many major features of the regular and chaotic motion. In this paper, we show that an algebraically simple system, the Genesio system can be recast into a jerky dynamics and its jerk equation can be derived from one-dimensional Newtonian equation. We also investigate the global dynamical properties of the corresponding jerk system.
基金Inner Mongolia University 2020 undergraduate teaching reform research and construction project-NDJG2094。
文摘This paper is concerned with the numerical dissipativity of multistep Runge-Kutta methods for nonlinear neutral delay-integro-differential equations.We investigate the dissipativity properties of-algebraically stable multistep Runge-Kutta methods with constrained grid.The finite-dimensional and infinite-dimensional dissipativity results of-algebraically stable multistep Runge-Kutta methods are obtained.
基金supported by National Natural Science Foundation of China (No. 11171125,91130003)Natural Science Foundation of Hubei (No. 2011CDB289)Youth Foundation of Naval University of Engineering (No.HGDQNJJ10003)
文摘This paper is concerned with the numerical dissipativity of multistep Runge-Kutta methods for nonlinear Volterra delay-integro-differential equations. We investigate the dissipativity properties of （k, l）- algebraically stable multistep Runge-Kutta methods with constrained grid and an uniform grid. The finite- dimensional and infinite-dimensional dissipativity results of （k, /）-algebraically stable Runge-Kutta methods are obtained.
