To study the Poisson theory of the generalized Birkhoff systems, the Lie algebra and the Poisson brackets were used to establish the Poisson theorem. The generalized Poisson condition for the first integral and the ge...To study the Poisson theory of the generalized Birkhoff systems, the Lie algebra and the Poisson brackets were used to establish the Poisson theorem. The generalized Poisson condition for the first integral and the generalized Poisson theorem of the generalized Birkhoff systems are obtained. An example is given to illustrate the application of the result.展开更多
For a class of quintic systems, the first 16 critical point quantities are obtained by computer algebraic system Mathematica, and the necessary and sufficient conditions that there exists an exact integral in a neighb...For a class of quintic systems, the first 16 critical point quantities are obtained by computer algebraic system Mathematica, and the necessary and sufficient conditions that there exists an exact integral in a neighborhood of the origin are also given. The technique employed is essentially different from usual ones. The recursive formula for computation of critical point quantities is linear and then avoids complex integral operations. Some results show an interesting contrast with the related results on quadratic systems.展开更多
Technically, when dealing with a perfect crystal, methods （PBC） in conjunction with plane-wave basis sets are widely in k-（reciprocal） space that impose periodic boundary conditions used. Chemists, however, tend t...Technically, when dealing with a perfect crystal, methods （PBC） in conjunction with plane-wave basis sets are widely in k-（reciprocal） space that impose periodic boundary conditions used. Chemists, however, tend to think of a solid as a giant mole- cule, which offers a molecular way to describe a solid by using a finite cluster model （FCM）. However, FCM may fail to sim- ulate a perfect crystal due to its inevitable boundary effects. We propose an RRS-PBC method that extracts the k-space infor- mation of a perfect crystalline solid out of a reduced real space （RRS） of an FCM. We show that the inevitable boundary effects in an FCM are eliminated naturally to achieve converged high-quality band structures.展开更多
In this paper, the target aggregation is investigated for a multi-agent system consisting of second-order agents and multiple leaders. Sufficient conditions are proposed to make the agents approach the target set span...In this paper, the target aggregation is investigated for a multi-agent system consisting of second-order agents and multiple leaders. Sufficient conditions are proposed to make the agents approach the target set spanned by these moving leaders. With the condition on switching interconnection topologies, all mobile agents can asymptotically track the dynamical target set specified by multiple moving leaders with bounded error. Moreover, discussion on the case with static leaders is also given.展开更多
This paper is focused on formability of multi-agent systems （MASs）. The problem is concerned with the existence of a protocol that has the ability to drive the MAS involved to the desired formation, and thus, is of ...This paper is focused on formability of multi-agent systems （MASs）. The problem is concerned with the existence of a protocol that has the ability to drive the MAS involved to the desired formation, and thus, is of essential importance in designing formation protocols. Formability of an MAS depends on several key factors： agents＇ dynamic structures, connectivity topology, properties of the desired formation and the admissible control set. Agents of the MASs considered here are described by a general continuous linear time-invariant （LTI） model. By using the matrix analysis and algebraic graph theory, some necessary and sufficient conditions on formability of LTI-MASs are obtained. These conditions characterize in some sense the relationship of formability, connectivity topology, formation properties and agent dynamics with respect to some typical and widely used admissible protocol sets.展开更多
文摘To study the Poisson theory of the generalized Birkhoff systems, the Lie algebra and the Poisson brackets were used to establish the Poisson theorem. The generalized Poisson condition for the first integral and the generalized Poisson theorem of the generalized Birkhoff systems are obtained. An example is given to illustrate the application of the result.
文摘For a class of quintic systems, the first 16 critical point quantities are obtained by computer algebraic system Mathematica, and the necessary and sufficient conditions that there exists an exact integral in a neighborhood of the origin are also given. The technique employed is essentially different from usual ones. The recursive formula for computation of critical point quantities is linear and then avoids complex integral operations. Some results show an interesting contrast with the related results on quadratic systems.
基金sponsored by the National Natural Science Foundation of China(21133004,91027044)the National Basic Research Program of China(2013CB834606,2011CB808505)the Swedish Research Council,and the Swedish National Infrastructure for Computing
文摘Technically, when dealing with a perfect crystal, methods （PBC） in conjunction with plane-wave basis sets are widely in k-（reciprocal） space that impose periodic boundary conditions used. Chemists, however, tend to think of a solid as a giant mole- cule, which offers a molecular way to describe a solid by using a finite cluster model （FCM）. However, FCM may fail to sim- ulate a perfect crystal due to its inevitable boundary effects. We propose an RRS-PBC method that extracts the k-space infor- mation of a perfect crystalline solid out of a reduced real space （RRS） of an FCM. We show that the inevitable boundary effects in an FCM are eliminated naturally to achieve converged high-quality band structures.
基金supported in part by the National Natural Science Foundation of China under Grant Nos. 60874018,60736022,and 60821091
文摘In this paper, the target aggregation is investigated for a multi-agent system consisting of second-order agents and multiple leaders. Sufficient conditions are proposed to make the agents approach the target set spanned by these moving leaders. With the condition on switching interconnection topologies, all mobile agents can asymptotically track the dynamical target set specified by multiple moving leaders with bounded error. Moreover, discussion on the case with static leaders is also given.
基金supported by the National Nature Science Foundation of China under Grants Nos.60934006 and 61104136the Shandong Provincial Natural Science Foundation under Grant No.ZR2010FQ002+1 种基金the School Foundation of Qufu Normal University under Grant No.XJ200913the Scientific Research Foundation of Qufu Normal University
文摘This paper is focused on formability of multi-agent systems （MASs）. The problem is concerned with the existence of a protocol that has the ability to drive the MAS involved to the desired formation, and thus, is of essential importance in designing formation protocols. Formability of an MAS depends on several key factors： agents＇ dynamic structures, connectivity topology, properties of the desired formation and the admissible control set. Agents of the MASs considered here are described by a general continuous linear time-invariant （LTI） model. By using the matrix analysis and algebraic graph theory, some necessary and sufficient conditions on formability of LTI-MASs are obtained. These conditions characterize in some sense the relationship of formability, connectivity topology, formation properties and agent dynamics with respect to some typical and widely used admissible protocol sets.
