The stabilization and H∞ control of nonlinear differential algebraic systems (NDAS) are investigated using the Hamiltonian function method. Firstly, we put forward a novel dissipative Hamiltonian realization (DHR...The stabilization and H∞ control of nonlinear differential algebraic systems (NDAS) are investigated using the Hamiltonian function method. Firstly, we put forward a novel dissipative Hamiltonian realization (DHR) structure and give the condition to complete the Hamiltonian realization. Then, based on the DHR, we present a criterion for the stability analysis of NDAS and construct a stabilization controller for NDAS in absence of disturbances. Finally, for NDAS in presence of disturbances, the L2 gain is analyzed via generalized Hamilton-Jacobi inequality and an H∞ control strategy is constructed. The proposed stabilization and robust controller can effectively take advantage of the structural characteristics of NDAS and is simple in form.展开更多
In this paper, a parallel simulation algorithm for the control problem in differential algebraic system is presented. The error of the algorithm is estimated. The stability analysis is made for a model problem and the...In this paper, a parallel simulation algorithm for the control problem in differential algebraic system is presented. The error of the algorithm is estimated. The stability analysis is made for a model problem and the stability region is given. The numerical example demonstrates that the method is efficient.展开更多
We investigate the problem of growth order of solutions of a type of systems of non-linear algebraic differential equations, and extend some results of the growth order of solutions of algebraic differential equations...We investigate the problem of growth order of solutions of a type of systems of non-linear algebraic differential equations, and extend some results of the growth order of solutions of algebraic differential equations to systems of algebraic differential equations.展开更多
The second order Euler-Lagrange equations are transformed to a set of first order differential/algebraic equations, which are then transformed to state equations by using local parameterization. The corresponding disc...The second order Euler-Lagrange equations are transformed to a set of first order differential/algebraic equations, which are then transformed to state equations by using local parameterization. The corresponding discretization method is presented, and the results can be used to implementation of various numerical integration methods. A numerical example is presented finally.展开更多
Using Nevanlinna theory of the value distribution of meromorphic functions, the author investigates the problem of the growth of solutions of two types of algebraic differential equation and obtains some results.
Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized higher order algebraic differential equations.
This article investigates the algebraic differential independence concerning the Euler Γ-function and the function F in a certain class F which contains Dirichlet L-functions,L-functions in the extended Selberg class...This article investigates the algebraic differential independence concerning the Euler Γ-function and the function F in a certain class F which contains Dirichlet L-functions,L-functions in the extended Selberg class, or some periodic functions. We prove that the EulerΓ-function and the function F cannot satisfy any nontrivial algebraic differential equations whose coefficients are meromorphic functions Ø with ρ(Ø) < 1.展开更多
A symbolic computation method to decide whether the solutions to the system Of linear partial differential equation is complete via using differential algebra and characteristic set is presented. This is a mechanizati...A symbolic computation method to decide whether the solutions to the system Of linear partial differential equation is complete via using differential algebra and characteristic set is presented. This is a mechanization method, and it can be carried out on the computer in the Maple environment.展开更多
In this paper, by means of the normal family theory, we estimate the growth order of meromorphic solutions of some algebraic differential equations and improve the related result of Barsegian et al. [6]. We also give ...In this paper, by means of the normal family theory, we estimate the growth order of meromorphic solutions of some algebraic differential equations and improve the related result of Barsegian et al. [6]. We also give some examples to show that our results occur in some special cases.展开更多
In this article, we give a simple proof of Malmquist-Yosida type theorem of higher order algebraic differential equations, which is different from the methods as that of Gackstatter and Laine [2], and Steinmetz [12].
Because homology on compact homogeneous nilpotent manifolds is closely related to homology on Lie algebras, studying homology on Lie algebras is helpful for further studying homology on compact homogeneous nilpotent m...Because homology on compact homogeneous nilpotent manifolds is closely related to homology on Lie algebras, studying homology on Lie algebras is helpful for further studying homology on compact homogeneous nilpotent manifolds. So we start with the differential sequence of Lie algebras. The Lie algebra g has the differential sequence E0,E1,⋯,Es⋯, which leads to the chain complex Es0→Δs0Ess→Δs1⋯→ΔsiEs(i+1)s→Δsi+1⋯of Esby discussing the chain complex E10→Δ10E11→Δ11⋯→Δ1r−1E1r→Δ1r⋯of E1and proves that Es+1i≅Hi(Es)=KerΔsi+1/ImΔsiand therefore Es+1≅H(Es)by the chain complex of Es(see Theorem 2).展开更多
In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarant...In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarantee of computations with a given precision. The equations of programmed constraints and those of constraint perturbations are defined. The stability of the programmed manifold for numerical solutions of the kinematical and dynamical equations is obtained by corresponding construction of the constraint perturbation equations. The dynamical equations of system with programmed constraints are set up in the form of Lagrange’s equations in generalized coordinates. Certain inverse problems of rigid body dynamics are examined.展开更多
In this paper,we study the algebraic differential and the difference independence between the Riemann zeta function and the Euler gamma function.It is proved that the Riemann zeta function and the Euler gamma function...In this paper,we study the algebraic differential and the difference independence between the Riemann zeta function and the Euler gamma function.It is proved that the Riemann zeta function and the Euler gamma function cannot satisfy a class of nontrivial algebraic differential equations and algebraic difference equations.展开更多
The subsystem synthesis method has been developed in order to improve computational efficiency for a multibody vehicle dynamics model. Using the subsystem synthesis method, equations of motion of the base body and eac...The subsystem synthesis method has been developed in order to improve computational efficiency for a multibody vehicle dynamics model. Using the subsystem synthesis method, equations of motion of the base body and each subsystem can be solved separately. In the subsystem synthesis method, various coordinate systems can be used and various integration methods can be applied in each subsystem, as long as the effective mass matrix and the effective force vector are properly produced. In this paper, comparative study has been carried out for the subsystem synthesis method with Cartesian coordinates and with joint relative coordinates. Two different integration methods such as an explicit integrator and an explicit implicit integrator are employed. In order to see the accuracy and computational efficiency from the different models based on the different coordinate systems and different integration methods, a rough terrain run simulations has been carried out with a 6 × 6 off-road multibody vehicle model.展开更多
In this paper, we give an estimate result of Gol'dberg's theorem concern- ing the growth of meromorphic solutions of Mgebraic differential equations by using Zalcman Lemma. It is an extending result of the correspon...In this paper, we give an estimate result of Gol'dberg's theorem concern- ing the growth of meromorphic solutions of Mgebraic differential equations by using Zalcman Lemma. It is an extending result of the corresponding theorem by Yuan et al. (Yuan W J, Xiao B, Zhang J J. The general theorem of Gol'dberg concerning the growth of meromorphic solutions of algebraic differential equations. Comput. Math. Appl., 2009, 58:1788 1791). Meanwhile, we also take some examples to show that our estimate is sharp.展开更多
We propose a novel computational framework that is capable of employing different time integration algorithms and different space discretized methods such as the Finite Element Method,particle methods,and other spatia...We propose a novel computational framework that is capable of employing different time integration algorithms and different space discretized methods such as the Finite Element Method,particle methods,and other spatial methods on a single body sub-dividedintomultiple subdomains.This is in conjunctionwithimplementing thewell known Generalized Single Step Single Solve(GS4)family of algorithms which encompass the entire scope of Linear Multistep algorithms that have been developed over the past 50 years or so and are second order accurate into the Differential Algebraic Equation framework.In the current state of technology,the coupling of altogether different time integration algorithms has been limited to the same family of algorithms such as theNewmarkmethods and the coupling of different algorithms usually has resulted in reduced accuracy in one or more variables including the Lagrange multiplier.However,the robustness and versatility of the GS4 with its ability to accurately account for the numerical shifts in various time schemes it encompasses,overcomes such barriers and allows a wide variety of arbitrary implicit-implicit,implicit-explicit,and explicit-explicit pairing of the various time schemes while maintaining the second order accuracy in time for not only all primary variables such as displacement,velocity and acceleration but also the Lagrange multipliers used for coupling the subdomains.By selecting an appropriate spatialmethod and time scheme on the area with localized phenomena contrary to utilizing a single process on the entire body,the proposed work has the potential to better capture the physics of a given simulation.The method is validated by solving 2D problems for the linear second order systems with various combination of spatial methods and time schemes with great flexibility.The accuracy and efficacy of the present work have not yet been seen in the current field,and it has shown significant promise in its capabilities and effectiveness for general linear dynamics through numerical examples.展开更多
This paper considers the class of autonomous algebraic ordinary differential equations(AODEs)of order one,and studies their Liouvillian general solutions.In particular,let F(y,w)=0 be a rational algebraic curve over C...This paper considers the class of autonomous algebraic ordinary differential equations(AODEs)of order one,and studies their Liouvillian general solutions.In particular,let F(y,w)=0 be a rational algebraic curve over C.The authors give necessary and sufficient conditions for the autonomous first-order AODE F(y,y′)=0 to have a Liouvillian solution over C.Moreover,the authors show that a Liouvillian solutionαof this equation is either an algebraic function over C(x)or an algebraic function over C(exp(ax)).As a byproduct,these results lead to an algorithm for determining a Liouvillian general solution of an autonomous AODE of order one of genus zero.Rational parametrizations of rational algebraic curves play an important role on this method.展开更多
For any K-algebra A,based on Hochschild complex and Hochschild coho-mology of A,we construct a new Gerstenhaber algebra,and give Gerstenhaber algebra epimorphism from the new Gerstenhaber algebra to the Gerstenhaber a...For any K-algebra A,based on Hochschild complex and Hochschild coho-mology of A,we construct a new Gerstenhaber algebra,and give Gerstenhaber algebra epimorphism from the new Gerstenhaber algebra to the Gerstenhaber algebra of the Hochschild cohomology of A.展开更多
An algebraic differential variety is defined as the zero-set of a differentialpolynomial set,and algebraic differential geometry is devoted to the study of such varieties.We give various decomposition formulas for the...An algebraic differential variety is defined as the zero-set of a differentialpolynomial set,and algebraic differential geometry is devoted to the study of such varieties.We give various decomposition formulas for the structures of such zero-sets which imply inparticular,the unique decomposition of an algebraic differential variety into its irreduciblecomponents.These formulas will find applications in various directions including mechanicaltheorem-proving of differential geometries.展开更多
基金the National Natural Science Foundation of China (Grant Nos. 69774011 and 60433050).
文摘The stabilization and H∞ control of nonlinear differential algebraic systems (NDAS) are investigated using the Hamiltonian function method. Firstly, we put forward a novel dissipative Hamiltonian realization (DHR) structure and give the condition to complete the Hamiltonian realization. Then, based on the DHR, we present a criterion for the stability analysis of NDAS and construct a stabilization controller for NDAS in absence of disturbances. Finally, for NDAS in presence of disturbances, the L2 gain is analyzed via generalized Hamilton-Jacobi inequality and an H∞ control strategy is constructed. The proposed stabilization and robust controller can effectively take advantage of the structural characteristics of NDAS and is simple in form.
文摘In this paper, a parallel simulation algorithm for the control problem in differential algebraic system is presented. The error of the algorithm is estimated. The stability analysis is made for a model problem and the stability region is given. The numerical example demonstrates that the method is efficient.
基金supported by the Natural Science Foundationof China (10471065)the Natural Science Foundation of Guangdong Province (N04010474)
文摘We investigate the problem of growth order of solutions of a type of systems of non-linear algebraic differential equations, and extend some results of the growth order of solutions of algebraic differential equations to systems of algebraic differential equations.
文摘The second order Euler-Lagrange equations are transformed to a set of first order differential/algebraic equations, which are then transformed to state equations by using local parameterization. The corresponding discretization method is presented, and the results can be used to implementation of various numerical integration methods. A numerical example is presented finally.
基金The project Supported by NNSF of China(19971052)
文摘Using Nevanlinna theory of the value distribution of meromorphic functions, the author investigates the problem of the growth of solutions of two types of algebraic differential equation and obtains some results.
文摘Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized higher order algebraic differential equations.
基金by Basic and Advanced Research Project of CQCSTC(cstc2019jcyj-msxmX0107)Fundamental Research Funds of Chongqing University of Posts and Telecommunications(CQUPT:A2018-125).
文摘This article investigates the algebraic differential independence concerning the Euler Γ-function and the function F in a certain class F which contains Dirichlet L-functions,L-functions in the extended Selberg class, or some periodic functions. We prove that the EulerΓ-function and the function F cannot satisfy any nontrivial algebraic differential equations whose coefficients are meromorphic functions Ø with ρ(Ø) < 1.
文摘A symbolic computation method to decide whether the solutions to the system Of linear partial differential equation is complete via using differential algebra and characteristic set is presented. This is a mechanization method, and it can be carried out on the computer in the Maple environment.
基金supported by the NNSF of China(11101048)supported by the Tianyuan Youth Fund of the NNSF of China(11326083)+4 种基金the Shanghai University Young Teacher Training Program(ZZSDJ12020)the Innovation Program of Shanghai Municipal Education Commission(14YZ164)the Projects(13XKJC01)from the Leading Academic Discipline Project of Shanghai Dianji Universitysupported by the NNSF of China(11271090)the NSF of Guangdong Province(S2012010010121)
文摘In this paper, by means of the normal family theory, we estimate the growth order of meromorphic solutions of some algebraic differential equations and improve the related result of Barsegian et al. [6]. We also give some examples to show that our results occur in some special cases.
基金supported by the Jiangsu Overseas Research and Training Program for University Prominent Young and Middle-aged Teachers and PresidentsNatural Science Foundation of China(11671191,11426118)+1 种基金Natural Science Foundation of Jiangsu Province(BK20140767)Qing Lan Project of Jiangsu Province
文摘In this article, we give a simple proof of Malmquist-Yosida type theorem of higher order algebraic differential equations, which is different from the methods as that of Gackstatter and Laine [2], and Steinmetz [12].
文摘Because homology on compact homogeneous nilpotent manifolds is closely related to homology on Lie algebras, studying homology on Lie algebras is helpful for further studying homology on compact homogeneous nilpotent manifolds. So we start with the differential sequence of Lie algebras. The Lie algebra g has the differential sequence E0,E1,⋯,Es⋯, which leads to the chain complex Es0→Δs0Ess→Δs1⋯→ΔsiEs(i+1)s→Δsi+1⋯of Esby discussing the chain complex E10→Δ10E11→Δ11⋯→Δ1r−1E1r→Δ1r⋯of E1and proves that Es+1i≅Hi(Es)=KerΔsi+1/ImΔsiand therefore Es+1≅H(Es)by the chain complex of Es(see Theorem 2).
基金Supported by Russian Fund of Fund amental Investigations(Pr.990101064)and Russian Minister of Educatin
文摘In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarantee of computations with a given precision. The equations of programmed constraints and those of constraint perturbations are defined. The stability of the programmed manifold for numerical solutions of the kinematical and dynamical equations is obtained by corresponding construction of the constraint perturbation equations. The dynamical equations of system with programmed constraints are set up in the form of Lagrange’s equations in generalized coordinates. Certain inverse problems of rigid body dynamics are examined.
基金supported by Basic and Advanced Research Project of CQ CSTC(cstc2019jcyj-msxmX0107)the Science and Technology Research Program of Chongqing Municipal Education Commission(KJQN202000621)Fundamental Research Funds of Chongqing University of Posts and Telecommunications(CQUPT:A2018-125)。
文摘In this paper,we study the algebraic differential and the difference independence between the Riemann zeta function and the Euler gamma function.It is proved that the Riemann zeta function and the Euler gamma function cannot satisfy a class of nontrivial algebraic differential equations and algebraic difference equations.
基金supported from by Unmanned Technology Research Center (UTRC) at Korea Advanced Institute of Science and Technology (KAIST),originally funded by DAPA,ADD
文摘The subsystem synthesis method has been developed in order to improve computational efficiency for a multibody vehicle dynamics model. Using the subsystem synthesis method, equations of motion of the base body and each subsystem can be solved separately. In the subsystem synthesis method, various coordinate systems can be used and various integration methods can be applied in each subsystem, as long as the effective mass matrix and the effective force vector are properly produced. In this paper, comparative study has been carried out for the subsystem synthesis method with Cartesian coordinates and with joint relative coordinates. Two different integration methods such as an explicit integrator and an explicit implicit integrator are employed. In order to see the accuracy and computational efficiency from the different models based on the different coordinate systems and different integration methods, a rough terrain run simulations has been carried out with a 6 × 6 off-road multibody vehicle model.
基金The NSF(10471065)of Chinathe Foundation(2011SQRL172)of the Education Department of Anhui Province for Outstanding Young Teachers in Universitythe Foundation(2012xq26)of the Huaibei Normal University for Young Teachers
文摘In this paper, we give an estimate result of Gol'dberg's theorem concern- ing the growth of meromorphic solutions of Mgebraic differential equations by using Zalcman Lemma. It is an extending result of the corresponding theorem by Yuan et al. (Yuan W J, Xiao B, Zhang J J. The general theorem of Gol'dberg concerning the growth of meromorphic solutions of algebraic differential equations. Comput. Math. Appl., 2009, 58:1788 1791). Meanwhile, we also take some examples to show that our estimate is sharp.
文摘We propose a novel computational framework that is capable of employing different time integration algorithms and different space discretized methods such as the Finite Element Method,particle methods,and other spatial methods on a single body sub-dividedintomultiple subdomains.This is in conjunctionwithimplementing thewell known Generalized Single Step Single Solve(GS4)family of algorithms which encompass the entire scope of Linear Multistep algorithms that have been developed over the past 50 years or so and are second order accurate into the Differential Algebraic Equation framework.In the current state of technology,the coupling of altogether different time integration algorithms has been limited to the same family of algorithms such as theNewmarkmethods and the coupling of different algorithms usually has resulted in reduced accuracy in one or more variables including the Lagrange multiplier.However,the robustness and versatility of the GS4 with its ability to accurately account for the numerical shifts in various time schemes it encompasses,overcomes such barriers and allows a wide variety of arbitrary implicit-implicit,implicit-explicit,and explicit-explicit pairing of the various time schemes while maintaining the second order accuracy in time for not only all primary variables such as displacement,velocity and acceleration but also the Lagrange multipliers used for coupling the subdomains.By selecting an appropriate spatialmethod and time scheme on the area with localized phenomena contrary to utilizing a single process on the entire body,the proposed work has the potential to better capture the physics of a given simulation.The method is validated by solving 2D problems for the linear second order systems with various combination of spatial methods and time schemes with great flexibility.The accuracy and efficacy of the present work have not yet been seen in the current field,and it has shown significant promise in its capabilities and effectiveness for general linear dynamics through numerical examples.
基金supported by Vietnam National Foundation for Science and Technology Development(NAFOSTED)under Grant No.101.04-2017.312。
文摘This paper considers the class of autonomous algebraic ordinary differential equations(AODEs)of order one,and studies their Liouvillian general solutions.In particular,let F(y,w)=0 be a rational algebraic curve over C.The authors give necessary and sufficient conditions for the autonomous first-order AODE F(y,y′)=0 to have a Liouvillian solution over C.Moreover,the authors show that a Liouvillian solutionαof this equation is either an algebraic function over C(x)or an algebraic function over C(exp(ax)).As a byproduct,these results lead to an algorithm for determining a Liouvillian general solution of an autonomous AODE of order one of genus zero.Rational parametrizations of rational algebraic curves play an important role on this method.
基金Supported by the National Natural Science Foundation of China(Grant No.12201182).
文摘For any K-algebra A,based on Hochschild complex and Hochschild coho-mology of A,we construct a new Gerstenhaber algebra,and give Gerstenhaber algebra epimorphism from the new Gerstenhaber algebra to the Gerstenhaber algebra of the Hochschild cohomology of A.
文摘An algebraic differential variety is defined as the zero-set of a differentialpolynomial set,and algebraic differential geometry is devoted to the study of such varieties.We give various decomposition formulas for the structures of such zero-sets which imply inparticular,the unique decomposition of an algebraic differential variety into its irreduciblecomponents.These formulas will find applications in various directions including mechanicaltheorem-proving of differential geometries.