In this paper we present a new version of Chen＇s system： a piecewise linear （PWL） Chert system of fractional-order. Via a sigmoid-like function, the discontinuous system is transformed into a continuous system. By...In this paper we present a new version of Chen＇s system： a piecewise linear （PWL） Chert system of fractional-order. Via a sigmoid-like function, the discontinuous system is transformed into a continuous system. By numerical simulations, we reveal chaotic behaviors and also multistability, i.e., the existence of small pararheter windows where, for some fixed bifurcation parameter and depending on initial conditions, coexistence of stable attractors and chaotic attractors is possible. Moreover, we show that by using an algorithm to switch the bifurcation parameter, the stable attractors can be numerically approximated.展开更多
In this paper, we consider the reconstruction of the wave field in a bounded domain. By choosing a special family of functions, the Cauchy problem can be transformed into a Fourier moment problem. This problem is ill-...In this paper, we consider the reconstruction of the wave field in a bounded domain. By choosing a special family of functions, the Cauchy problem can be transformed into a Fourier moment problem. This problem is ill-posed. We propose a regularization method for obtaining an approximate solution to the wave field on the unspecified boundary. We also give the convergence analysis and error estimate of the numerical algorithm. Finally, we present some numerical examples to show the effectiveness of this method.展开更多
It is increasingly common to find graphs in which edges are of different types, indicating a variety of relation- ships. For such graphs we propose a class of reachability queries and a class of graph patterns, in whi...It is increasingly common to find graphs in which edges are of different types, indicating a variety of relation- ships. For such graphs we propose a class of reachability queries and a class of graph patterns, in which an edge is specified with a regular expression of a certain form, ex- pressing the connectivity of a data graph via edges of var- ious types. In addition, we define graph pattern matching based on a revised notion of graph simulation. On graphs in emerging applications such as social networks, we show that these queries are capable of finding more sensible informa- tion than their traditional counterparts. Better still, their in- creased expressive power does not come with extra complex- ity. Indeed, （1） we investigate their containment and mini- mization problems, and show that these fundamental prob- lems are in quadratic time for reachability queries and are in cubic time for pattern queries. （2） We develop an algorithm for answering reachability queries, in quadratic time as for their traditional counterpart. （3） We provide two cubic-time algorithms for evaluating graph pattern queries, as opposed to the NP-completeness of graph pattern matching via subgraph isomorphism. （4） The effectiveness and efficiency of these al- gorithms are experimentally verified using real-life data and synthetic data.展开更多
Adaptive finite element methods for optimization problems for second order linear el- liptic partial differential equations subject to pointwise constraints on the l2-norm of the gradient of the state are considered. ...Adaptive finite element methods for optimization problems for second order linear el- liptic partial differential equations subject to pointwise constraints on the l2-norm of the gradient of the state are considered. In a weak duality setting, i.e. without assuming a constraint qualification such as the existence of a Slater point, residual based a posteriori error estimators are derived. To overcome the lack in constraint qualification on the continuous level, the weak Fenchel dual is utilized. Several numerical tests illustrate the performance of the proposed error estimators.Mathematics subject classification： 65N30, 90C46, 65N50, 49K20, 49N15, 65K10.展开更多
基金funded by the European Regional Development Funding via RISC projectby CPER Region Haute Normandie France,the Australian Research Council via a Future Fellowship(FT110100896)Discovery Project(DP140100203)
文摘In this paper we present a new version of Chen＇s system： a piecewise linear （PWL） Chert system of fractional-order. Via a sigmoid-like function, the discontinuous system is transformed into a continuous system. By numerical simulations, we reveal chaotic behaviors and also multistability, i.e., the existence of small pararheter windows where, for some fixed bifurcation parameter and depending on initial conditions, coexistence of stable attractors and chaotic attractors is possible. Moreover, we show that by using an algorithm to switch the bifurcation parameter, the stable attractors can be numerically approximated.
文摘In this paper, we consider the reconstruction of the wave field in a bounded domain. By choosing a special family of functions, the Cauchy problem can be transformed into a Fourier moment problem. This problem is ill-posed. We propose a regularization method for obtaining an approximate solution to the wave field on the unspecified boundary. We also give the convergence analysis and error estimate of the numerical algorithm. Finally, we present some numerical examples to show the effectiveness of this method.
文摘It is increasingly common to find graphs in which edges are of different types, indicating a variety of relation- ships. For such graphs we propose a class of reachability queries and a class of graph patterns, in which an edge is specified with a regular expression of a certain form, ex- pressing the connectivity of a data graph via edges of var- ious types. In addition, we define graph pattern matching based on a revised notion of graph simulation. On graphs in emerging applications such as social networks, we show that these queries are capable of finding more sensible informa- tion than their traditional counterparts. Better still, their in- creased expressive power does not come with extra complex- ity. Indeed, （1） we investigate their containment and mini- mization problems, and show that these fundamental prob- lems are in quadratic time for reachability queries and are in cubic time for pattern queries. （2） We develop an algorithm for answering reachability queries, in quadratic time as for their traditional counterpart. （3） We provide two cubic-time algorithms for evaluating graph pattern queries, as opposed to the NP-completeness of graph pattern matching via subgraph isomorphism. （4） The effectiveness and efficiency of these al- gorithms are experimentally verified using real-life data and synthetic data.
文摘Adaptive finite element methods for optimization problems for second order linear el- liptic partial differential equations subject to pointwise constraints on the l2-norm of the gradient of the state are considered. In a weak duality setting, i.e. without assuming a constraint qualification such as the existence of a Slater point, residual based a posteriori error estimators are derived. To overcome the lack in constraint qualification on the continuous level, the weak Fenchel dual is utilized. Several numerical tests illustrate the performance of the proposed error estimators.Mathematics subject classification： 65N30, 90C46, 65N50, 49K20, 49N15, 65K10.
