Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting...Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.展开更多
In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality...In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality,this inequality contains a term involving the mean curvature.展开更多
This paper is concerned with the parabolic-parabolic-elliptic system■in a bounded domainΩ?Rnwith a smooth boundary,where the parametersχ,ζ1,ζ2are positive constants and m≥1.Based on the coupled energy estimates,...This paper is concerned with the parabolic-parabolic-elliptic system■in a bounded domainΩ?Rnwith a smooth boundary,where the parametersχ,ζ1,ζ2are positive constants and m≥1.Based on the coupled energy estimates,the boundedness of the global classical solution is established in any dimensions(n≥1)provided that m>1.展开更多
This paper deals with the supervisory control problem of discrete event systems modeled by labeled Petri nets. The system is originally unbounded. First, the solvability of the problem is confirmed. A necessary condit...This paper deals with the supervisory control problem of discrete event systems modeled by labeled Petri nets. The system is originally unbounded. First, the solvability of the problem is confirmed. A necessary condition is given and proven for the existence of a feasible priority-based controller based on the notions of liveness and transition invariants. Next, a cyclic behavior graph is constructed, which shows the reachable markings that guarantee the maximum liveness of the system within a given bound vector. Finally, an on-line control strategy is proposed to enforce boundedness and liveness to the given system by appending priority relations to transitions. The dynamic priority relation changes flexibly according to the current state of the system and enforces the system evolving in a bounded and live manner. In addition, numerical examples are studied to verify the validity of the proposed approach that remains the structure of the plant net and is efficient for on-line control.展开更多
We study types of boundedness of a semigroup on a Banach space in terms of the Cesáro-average and the behavior of the resolvent at the origin and also exhibit a characterization of type Hille-Yosida for the gener...We study types of boundedness of a semigroup on a Banach space in terms of the Cesáro-average and the behavior of the resolvent at the origin and also exhibit a characterization of type Hille-Yosida for the generators of ϕ<sup>j</sup>-bounded strongly continuous semigroups. Furthermore, these results are used to investigate the effect of the Perturbation on the type of the growth of sequences.展开更多
This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their...This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their expressions and asymptotical stability criteria.Second,for the semi-discrete and one-parameter fully-discrete finite element methods solving the above equations,we work out the sufficient conditions for assuring that the finite element solutions are asymptotically stable.Finally,with a typical example with numerical experiments,we illustrate the applicability of the obtained theoretical results.展开更多
文摘Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.
基金Supported by the NSFC(11771087,12171091 and 11831005)。
文摘In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality,this inequality contains a term involving the mean curvature.
基金supported by the NSF of China(11871226)Guangdong Basic and Applied Basic Research Foundation(2020A1515010140 and 2022B1515020032)Guangzhou Science and Technology Program(202002030363)。
文摘This paper is concerned with the parabolic-parabolic-elliptic system■in a bounded domainΩ?Rnwith a smooth boundary,where the parametersχ,ζ1,ζ2are positive constants and m≥1.Based on the coupled energy estimates,the boundedness of the global classical solution is established in any dimensions(n≥1)provided that m>1.
基金the Project of Industrial Internet and Integration of Industrialization and Industrialization of Guangxi,China under Grant No.Guigong2021-37.
文摘This paper deals with the supervisory control problem of discrete event systems modeled by labeled Petri nets. The system is originally unbounded. First, the solvability of the problem is confirmed. A necessary condition is given and proven for the existence of a feasible priority-based controller based on the notions of liveness and transition invariants. Next, a cyclic behavior graph is constructed, which shows the reachable markings that guarantee the maximum liveness of the system within a given bound vector. Finally, an on-line control strategy is proposed to enforce boundedness and liveness to the given system by appending priority relations to transitions. The dynamic priority relation changes flexibly according to the current state of the system and enforces the system evolving in a bounded and live manner. In addition, numerical examples are studied to verify the validity of the proposed approach that remains the structure of the plant net and is efficient for on-line control.
文摘We study types of boundedness of a semigroup on a Banach space in terms of the Cesáro-average and the behavior of the resolvent at the origin and also exhibit a characterization of type Hille-Yosida for the generators of ϕ<sup>j</sup>-bounded strongly continuous semigroups. Furthermore, these results are used to investigate the effect of the Perturbation on the type of the growth of sequences.
文摘This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their expressions and asymptotical stability criteria.Second,for the semi-discrete and one-parameter fully-discrete finite element methods solving the above equations,we work out the sufficient conditions for assuring that the finite element solutions are asymptotically stable.Finally,with a typical example with numerical experiments,we illustrate the applicability of the obtained theoretical results.
