This paper focuses on studying a new energy-work relationship numericM integration scheme of nonholonomic Hamiltonian systems. The signal-stage numerical, multi-stage and parallel composition numerical integration sch...This paper focuses on studying a new energy-work relationship numericM integration scheme of nonholonomic Hamiltonian systems. The signal-stage numerical, multi-stage and parallel composition numerical integration schemes are presented. The high-order energy-work relation scheme of the system is constructed by a parallel connection of n multi-stage schemes of order 2, its order of accuracy is 2n. The connection, which is discrete analogue of usual case, between the change of energy and work of nonholonomic constraint forces is obtained for nonholonomie Hamiltonian systems. This paper also gives that there is smaller error of the scheme when taking a large number of stages than a less one. Finally, an applied example is discussed to illustrate these results.展开更多
The basic principle of interval arithmetic and the basic algorithm of the interval Newton methods are introduced.The prototype algorithm can not find any zero in an interval that has zero sometimes,that is,it is insta...The basic principle of interval arithmetic and the basic algorithm of the interval Newton methods are introduced.The prototype algorithm can not find any zero in an interval that has zero sometimes,that is,it is instable.So the prototype relaxation procedure is improved in this paper.Additionally,an immediate test of the existence of a solution following branch_and_bound is proposed,which avoids unwanted computations in those intervals that have no solution.The numerical results demonstrat that the improved interval Newton method is superior to prototype algorithm in terms of solution quality,stability and convergent speed.展开更多
An ensemble adjustment Kalman filter system is developed to assimilate Argo profiles into the Northwest Pacific MASNUM wave-circulation coupled model, which is based on the Princeton Ocean Model (POM). This model was ...An ensemble adjustment Kalman filter system is developed to assimilate Argo profiles into the Northwest Pacific MASNUM wave-circulation coupled model, which is based on the Princeton Ocean Model (POM). This model was recoded in FORTRAN-90 style, and some new data types were defined to improve the efficiency of system design and execution. This system is arranged for parallel computing by using UNIX shell scripts: it is easier with single models running separately with the required information exchanged through input/output files. Tests are carried out to check the performance of the system: one for checking the ensemble spread and another for the performance of assimilation of the Argo data in 2005. The first experiment shows that the assimilation system performs well. The comparison with the Satellite derived sea surface temperature (SST) shows that modeled SST errors are reduced after assimilation; at the same time, the spatial correlation between the simulated SST anomalies and the satellite data is improved because of Argo assimilation. Furthermore, the temporal evolution/trend of SST becomes much better than those results without data assimilation. The comparison against GTSPP profiles shows that the improvement is not only in the upper layers of ocean, but also in the deeper layers. All these results suggest that this system is potentially capable of reconstructing oceanic data sets that are of high quality and are temporally and spatially continuous.展开更多
For non-negative integers i,j and k,let N i,j,k be the graph obtained by identifying end vertices of three disjoint paths of lengths i,j and k to the vertices of a triangle.In this paper,we prove that every 3-connecte...For non-negative integers i,j and k,let N i,j,k be the graph obtained by identifying end vertices of three disjoint paths of lengths i,j and k to the vertices of a triangle.In this paper,we prove that every 3-connected {K1,3,N3,3,3 }-free graph is Hamiltonian.This result is sharp in the sense that for any integer i>3,there exist infinitely many 3-connected {K1,3,Ni,3,3 }-free non-Hamiltonian graphs.展开更多
The purpose of tthis note is to study a convergence for a method in form of combinationo f discrete approximations with regularization for solving operator equations of Hammerstein’stype in Banach spaces. FOr illustr...The purpose of tthis note is to study a convergence for a method in form of combinationo f discrete approximations with regularization for solving operator equations of Hammerstein’stype in Banach spaces. FOr illustration, an example in the theory of nonlinear integral equationsis given.展开更多
A geometric setting for generally nonconservative mechanical systems on fibred manifolds is proposed. Emphasis is put on an explicit formulation of nonholonomic mechanics when an unconstrained Lagrangian system moves ...A geometric setting for generally nonconservative mechanical systems on fibred manifolds is proposed. Emphasis is put on an explicit formulation of nonholonomic mechanics when an unconstrained Lagrangian system moves in a generally non-potential force field depending on time, positions and velocities, and the constraints are nonholonomic, not necessarily linear in velocities. Equations of motion, and the corresponding Harniltonian equations in intrinsic form are given. Regularity conditions are found and a nonholonomic Legendre transformation is proposed, leading to a canonical form of the nonholonomic Hamiltonian equations for nonconservative systems.展开更多
基金supported by National Natural Science Foundation of China under Grant No.10672143the Natural Science Foundation of Henan Province under Grant No.0511022200
文摘This paper focuses on studying a new energy-work relationship numericM integration scheme of nonholonomic Hamiltonian systems. The signal-stage numerical, multi-stage and parallel composition numerical integration schemes are presented. The high-order energy-work relation scheme of the system is constructed by a parallel connection of n multi-stage schemes of order 2, its order of accuracy is 2n. The connection, which is discrete analogue of usual case, between the change of energy and work of nonholonomic constraint forces is obtained for nonholonomie Hamiltonian systems. This paper also gives that there is smaller error of the scheme when taking a large number of stages than a less one. Finally, an applied example is discussed to illustrate these results.
文摘The basic principle of interval arithmetic and the basic algorithm of the interval Newton methods are introduced.The prototype algorithm can not find any zero in an interval that has zero sometimes,that is,it is instable.So the prototype relaxation procedure is improved in this paper.Additionally,an immediate test of the existence of a solution following branch_and_bound is proposed,which avoids unwanted computations in those intervals that have no solution.The numerical results demonstrat that the improved interval Newton method is superior to prototype algorithm in terms of solution quality,stability and convergent speed.
基金Supported by the Project of National Basic Research Program of China (No. 2007CB816002)Special Fund for Fundamental Scientific Research (No. 2008G08)
文摘An ensemble adjustment Kalman filter system is developed to assimilate Argo profiles into the Northwest Pacific MASNUM wave-circulation coupled model, which is based on the Princeton Ocean Model (POM). This model was recoded in FORTRAN-90 style, and some new data types were defined to improve the efficiency of system design and execution. This system is arranged for parallel computing by using UNIX shell scripts: it is easier with single models running separately with the required information exchanged through input/output files. Tests are carried out to check the performance of the system: one for checking the ensemble spread and another for the performance of assimilation of the Argo data in 2005. The first experiment shows that the assimilation system performs well. The comparison with the Satellite derived sea surface temperature (SST) shows that modeled SST errors are reduced after assimilation; at the same time, the spatial correlation between the simulated SST anomalies and the satellite data is improved because of Argo assimilation. Furthermore, the temporal evolution/trend of SST becomes much better than those results without data assimilation. The comparison against GTSPP profiles shows that the improvement is not only in the upper layers of ocean, but also in the deeper layers. All these results suggest that this system is potentially capable of reconstructing oceanic data sets that are of high quality and are temporally and spatially continuous.
基金supported by National Natural Science Foundation of China (Grant Nos.11071096 and 11271149)Hubei Provincial Department of Education (Grant No. D20111110)Jinan Science and Technology Bureau (Grant No. 20110205)
文摘For non-negative integers i,j and k,let N i,j,k be the graph obtained by identifying end vertices of three disjoint paths of lengths i,j and k to the vertices of a triangle.In this paper,we prove that every 3-connected {K1,3,N3,3,3 }-free graph is Hamiltonian.This result is sharp in the sense that for any integer i>3,there exist infinitely many 3-connected {K1,3,Ni,3,3 }-free non-Hamiltonian graphs.
文摘The purpose of tthis note is to study a convergence for a method in form of combinationo f discrete approximations with regularization for solving operator equations of Hammerstein’stype in Banach spaces. FOr illustration, an example in the theory of nonlinear integral equationsis given.
基金supported by the Czech Science Foundation (Grant No.GA CˇR 201/09/0981)the Czech-Hungarian Cooperation Programme "Kontakt" (Grant No. MEB041005)the IRSES project ’GEOMECH’ (Grant No. 246981) within the 7th European Community Framework Programme
文摘A geometric setting for generally nonconservative mechanical systems on fibred manifolds is proposed. Emphasis is put on an explicit formulation of nonholonomic mechanics when an unconstrained Lagrangian system moves in a generally non-potential force field depending on time, positions and velocities, and the constraints are nonholonomic, not necessarily linear in velocities. Equations of motion, and the corresponding Harniltonian equations in intrinsic form are given. Regularity conditions are found and a nonholonomic Legendre transformation is proposed, leading to a canonical form of the nonholonomic Hamiltonian equations for nonconservative systems.
