For a relativistic Birkhoflan system, the first integrals and the construction of integral invariants are studied. Firstly, the cyclic integrals and the generalized energy integral of the system are found by using the...For a relativistic Birkhoflan system, the first integrals and the construction of integral invariants are studied. Firstly, the cyclic integrals and the generalized energy integral of the system are found by using the perfect differential method. Secondly, the equations of nonsimultaneous variation of the system are established by using the relation between the simultaneous variation and the nonsimultaneous variation. Thirdly, the relation between the first integral and the integral invariant of the system is studied, and it is proved that, using a t^rst integral, we can construct an integral invarlant of the system. Finally, the relation between the relativistic Birkhoflan dynamics and the relativistic Hamilton;an dynamics is discussed, and the first integrals and the integral invariants of the relativistic Hamiltonian system are obtained. Two examples are given to illustrate the application of the results.展开更多
Using a complete discrimination system for polynomials, new exact traveling wave solutions for generalized Ginzburg-Landau equation are obtained. The method has general meaning for many similar problems.
By an established comparison result and using the upper and lower solutions,one sufficient condition of existence of minimal and maximal solutions to initial value problem for second order impulsive integro-differenti...By an established comparison result and using the upper and lower solutions,one sufficient condition of existence of minimal and maximal solutions to initial value problem for second order impulsive integro-differential equation in Banach spaces is obtained and the related results are essentially improved.At the same time, another sufficient condition of existence of minimal and maximal solutions based on the Kuratowski measure of noncompactness is given.展开更多
For linear partial differential equation 〔 2t 2-a 2P( x)〕 m u=f(x,t), where m1,X∈R n,t∈R 1, the author gives the analytic solution of the initial value problem using the operators sh(tP( x) 1/2 )...For linear partial differential equation 〔 2t 2-a 2P( x)〕 m u=f(x,t), where m1,X∈R n,t∈R 1, the author gives the analytic solution of the initial value problem using the operators sh(tP( x) 1/2 )P( x) 1/2 . By representing the operators with integrals, explicit solutions are obtained with an integral form of a given function.展开更多
In this paper we introduce an implementation for the efficient numericalsolution of exterior initial boundary value problem for parabolic equation. The problemis reformulated as an equivalent one on a boundary T using...In this paper we introduce an implementation for the efficient numericalsolution of exterior initial boundary value problem for parabolic equation. The problemis reformulated as an equivalent one on a boundary T using natural boundary reduction.The governing equation is first discretized in time, leading to a time-stepping scheme,where an exterior elliptic problem has to be solved in each time step. By Fourier ex-pansion, we derive a natural integral equation of the elliptic problem related to timestep and Poisson integral integral formula over exterior circular domain. Finite elementdiscretization of the natural integral equation is employed to solve this problem. Thecomputational aspects of this method are discussed. Numerical results are presented toillustrate feasibility and efficiency of our method.展开更多
This paper investigates the maximal and minimal solutions of initial value problem for n-th order nonlinear integro-differential equations of Volterra type on an infinite interval in a Banach space by establishing a c...This paper investigates the maximal and minimal solutions of initial value problem for n-th order nonlinear integro-differential equations of Volterra type on an infinite interval in a Banach space by establishing a comparison result and using the monotone iterative technique.展开更多
This paper presents a further development of the dual reciprocity boundary element method(DRBEM) with stepwise updating to pave the way for the introduction of boundary element mesh into the discontinuous deformation ...This paper presents a further development of the dual reciprocity boundary element method(DRBEM) with stepwise updating to pave the way for the introduction of boundary element mesh into the discontinuous deformation analysis(DDA). The advantage of the proposed method lies in its adoption of static fundamental solutions and reduction in the size of the governing equations by transforming the inertial term domain integrals to boundary integrals in the dynamic large displacement analysis. The unconditionally stable Newmark-β time integration method involving numerical damping to enhance the numerical stability is implemented for the dynamic analysis. In order to be coupled with the DDA to improve the deformability of the DDA block domains, a stepwise updating algorithm of the system variables is introduced. The stress updating in the analysis involved in the calculation of a domain integral and internal cells are used for the integration of the initial stress term. Several examples are used to verify the geometry-updated DRBEM model and satisfactory results have been obtained.展开更多
Quillen proved that if a Hermitian bihomogeneous polynomial is strictly positive on the unit sphere, then repeated multiplication of the standard sesquilinear form to this polynomial eventually results in a sum of Her...Quillen proved that if a Hermitian bihomogeneous polynomial is strictly positive on the unit sphere, then repeated multiplication of the standard sesquilinear form to this polynomial eventually results in a sum of Hermitian squares. Catlin-D'Angelo and Varolin deduced this positivstellensatz of Quillen from the eventual positive-definiteness of an associated integral operator. Their arguments involve asymptotic expansions of the Bergman kernel. The goal of this article is to give an elementary proof of the positive-definiteness of this integral operator.展开更多
文摘For a relativistic Birkhoflan system, the first integrals and the construction of integral invariants are studied. Firstly, the cyclic integrals and the generalized energy integral of the system are found by using the perfect differential method. Secondly, the equations of nonsimultaneous variation of the system are established by using the relation between the simultaneous variation and the nonsimultaneous variation. Thirdly, the relation between the first integral and the integral invariant of the system is studied, and it is proved that, using a t^rst integral, we can construct an integral invarlant of the system. Finally, the relation between the relativistic Birkhoflan dynamics and the relativistic Hamilton;an dynamics is discussed, and the first integrals and the integral invariants of the relativistic Hamiltonian system are obtained. Two examples are given to illustrate the application of the results.
文摘Using a complete discrimination system for polynomials, new exact traveling wave solutions for generalized Ginzburg-Landau equation are obtained. The method has general meaning for many similar problems.
文摘By an established comparison result and using the upper and lower solutions,one sufficient condition of existence of minimal and maximal solutions to initial value problem for second order impulsive integro-differential equation in Banach spaces is obtained and the related results are essentially improved.At the same time, another sufficient condition of existence of minimal and maximal solutions based on the Kuratowski measure of noncompactness is given.
文摘For linear partial differential equation 〔 2t 2-a 2P( x)〕 m u=f(x,t), where m1,X∈R n,t∈R 1, the author gives the analytic solution of the initial value problem using the operators sh(tP( x) 1/2 )P( x) 1/2 . By representing the operators with integrals, explicit solutions are obtained with an integral form of a given function.
基金National Natural Science Foundation of China(19701001)
文摘In this paper we introduce an implementation for the efficient numericalsolution of exterior initial boundary value problem for parabolic equation. The problemis reformulated as an equivalent one on a boundary T using natural boundary reduction.The governing equation is first discretized in time, leading to a time-stepping scheme,where an exterior elliptic problem has to be solved in each time step. By Fourier ex-pansion, we derive a natural integral equation of the elliptic problem related to timestep and Poisson integral integral formula over exterior circular domain. Finite elementdiscretization of the natural integral equation is employed to solve this problem. Thecomputational aspects of this method are discussed. Numerical results are presented toillustrate feasibility and efficiency of our method.
文摘This paper investigates the maximal and minimal solutions of initial value problem for n-th order nonlinear integro-differential equations of Volterra type on an infinite interval in a Banach space by establishing a comparison result and using the monotone iterative technique.
基金supported by the International Postgraduate Research Scholarship(IPRS)Australian Postgraduate Award(APA)sponsored by the Australian Government via the University of Western Australiathe National Natural Science Foundation of China(Grant Nos.41130751&51178012)
文摘This paper presents a further development of the dual reciprocity boundary element method(DRBEM) with stepwise updating to pave the way for the introduction of boundary element mesh into the discontinuous deformation analysis(DDA). The advantage of the proposed method lies in its adoption of static fundamental solutions and reduction in the size of the governing equations by transforming the inertial term domain integrals to boundary integrals in the dynamic large displacement analysis. The unconditionally stable Newmark-β time integration method involving numerical damping to enhance the numerical stability is implemented for the dynamic analysis. In order to be coupled with the DDA to improve the deformability of the DDA block domains, a stepwise updating algorithm of the system variables is introduced. The stress updating in the analysis involved in the calculation of a domain integral and internal cells are used for the integration of the initial stress term. Several examples are used to verify the geometry-updated DRBEM model and satisfactory results have been obtained.
文摘Quillen proved that if a Hermitian bihomogeneous polynomial is strictly positive on the unit sphere, then repeated multiplication of the standard sesquilinear form to this polynomial eventually results in a sum of Hermitian squares. Catlin-D'Angelo and Varolin deduced this positivstellensatz of Quillen from the eventual positive-definiteness of an associated integral operator. Their arguments involve asymptotic expansions of the Bergman kernel. The goal of this article is to give an elementary proof of the positive-definiteness of this integral operator.
