In this article, criteria of eventual stability are established for impulsive differential systems using piecewise continuous Lyapunov functions. The sufficient conditions that are obtained significantly depend on the...In this article, criteria of eventual stability are established for impulsive differential systems using piecewise continuous Lyapunov functions. The sufficient conditions that are obtained significantly depend on the moments of impulses. An example is discussed to illustrate the theorem.展开更多
In this paper,we approximate the solution and also discuss the periodic behavior termed as eventual periodicity of solutions of(IBVPs)for some dispersive wave equations on a bounded domain corresponding to periodic fo...In this paper,we approximate the solution and also discuss the periodic behavior termed as eventual periodicity of solutions of(IBVPs)for some dispersive wave equations on a bounded domain corresponding to periodic forcing.The constructed numerical scheme is based on radial kernels and local in nature like finite difference method.The temporal variable is executed through RK4 scheme.Due to the local nature and sparse differentiation matrices our numerical scheme efficiently recovers the solution.The results achieved are validated and examined with other methods accessible in the literature.展开更多
In this paper, we aim to find eventually vanished solutions, a special class of bounded solutions which tend to 0 as t → ±∞）, to a Lienard system with a time-dependent force. Since it is not a Hamiltonian syst...In this paper, we aim to find eventually vanished solutions, a special class of bounded solutions which tend to 0 as t → ±∞）, to a Lienard system with a time-dependent force. Since it is not a Hamiltonian system with small perturbations, the well-known Melnikov method is not applicable to the determination of the existence of eventually vanished solutions. We use a sequence of periodically forced systems to approximate the considered system, and find their periodic solutions. Difficulties caused by the non- Hamiltonian form are overcome by applying the Schauder＇s fixed point theorem. We show that the sequence of the periodic solutions has an accumulation giving an eventually vanished solution of the forced Lienard system.展开更多
it In this paper, the properties of set-valued Eventual Supermartingle are discussed. The main result is that suppose {Fn, n ≥ 1） Lfc^1（X） be set-valued Eventual Supermartingle, ifsupE（d（0,Fτ）） 〈 ∞, then ...it In this paper, the properties of set-valued Eventual Supermartingle are discussed. The main result is that suppose {Fn, n ≥ 1） Lfc^1（X） be set-valued Eventual Supermartingle, ifsupE（d（0,Fτ）） 〈 ∞, then Fn →KF and SF^1≠φ, here T is the sets of all T bounded stopping times.展开更多
The authors introduce the concepts of the eventual shadowing property and eventually shadowable point for set-valued dynamical systems and prove that a set-valued dynamical system has the eventual shadowing property i...The authors introduce the concepts of the eventual shadowing property and eventually shadowable point for set-valued dynamical systems and prove that a set-valued dynamical system has the eventual shadowing property if and only if every point in the phase space is eventually shadowable;every chain transitive set-valued dynamical system has either the eventual shadowing property or no eventually shadowable points;and a set-valued dynamical system admits an eventually shadowable point if and only if it admits a minimal eventually shadowable point.Moreover,it is proved that a set-valued dynamical system with the eventual shadowing property is chain mixing if and only if it is mixing and if and only if it has the specification property.展开更多
In this article,we provide some sufficient conditions for the dynamical systems with the eventual shadowing property to have positive topological entropy and several equivalent conditions for the dynamical systems wit...In this article,we provide some sufficient conditions for the dynamical systems with the eventual shadowing property to have positive topological entropy and several equivalent conditions for the dynamical systems with the eventual shadowing property to be mixing.展开更多
This paper considers the eventual leader election problem in asynchronous message-passing systems where an arbitrary number t of processes can crash（t〈n,where n is the total number of processes）.It considers weak a...This paper considers the eventual leader election problem in asynchronous message-passing systems where an arbitrary number t of processes can crash（t〈n,where n is the total number of processes）.It considers weak assumptions both on the initial knowledge of the processes and on the network behavior.More precisely,initially,a process knows only its identity and the fact that the process identities are different and totally ordered（it knows neither n nor t）.Two eventual leader election protocols and a lower bound are presented.The first protocol assumes that a process also knows a lower bound α on the number of processes that do not crash.This protocol requires the following behavioral properties from the underlying network：the graph made up of the correct processes and fair lossy links is strongly connected,and there is a correct process connected to（n〈f）-α other correct processes（where f is the actual number of crashes in the considered run） through eventually timely paths（paths made up of correct processes and eventually timely links）.This protocol is not communication-efficient in the sense that each correct process has to send messages forever.The second protocol is communication-efficient：after some time,only the final common leader has to send messages forever.This protocol does not require the processes to know α,but requires stronger properties from the underlying network：each pair of correct processes has to be connected by fair lossy links（one in each direction）,and there is a correct process whose n〈f-1 output links to the rest of correct processes have to be eventually timely.A matching lower bound result shows that any eventual leader election protocol must have runs with this number of eventually timely links,even if all processes know all the processes identities.In addition to being communication-efficient,the second protocol has another noteworthy efficiency property,namely,be the run finite or infinite,all the local variables and message fields have a finite domain in the run.展开更多
Data items are usually replicated in modem dis- tributed data stores to obtain high performance and avail- ability. However, the availability-consistency and latency- consistency trade-offs exist in data replication, ...Data items are usually replicated in modem dis- tributed data stores to obtain high performance and avail- ability. However, the availability-consistency and latency- consistency trade-offs exist in data replication, thus system designers intend to choose weak consistency models, such as eventual consistency, which may result in stale reads. Since stale data items may lead to serious application semantic problems, we consider how to increase the probability of data recency which provides a uniform view on recent versions of data items for all clients. In this work, we propose HARP, a framework that can enhance data recency of eventually con- sistent distributed data stores in an efficient and highly avail- able way. Through detecting possible stale reads under fail- ures or not, HARP can perform reread operations to elim- inate stale results only when needed based on our analysis on write/read processes. We also present solutions on how to deal with some practical anomalies in HARP, including de- layed, reordered and dropped messages and clock drift, and show how to extend HARP to multiple datacenters. Finally we implement HARP based on Cassandra, and the experi- ments show that HARP can effectively eliminate stale reads, with a low overhead （less than 6.9%） compared with original eventually consistent Cassandra.展开更多
We investigate some relations between two kinds of semigroup regularities, namely the e-property and the eventual continuity, both of which contribute to the ergodicity for Markov processes on Polish spaces.More preci...We investigate some relations between two kinds of semigroup regularities, namely the e-property and the eventual continuity, both of which contribute to the ergodicity for Markov processes on Polish spaces.More precisely, we prove that for Markov-Feller semigroup in discrete time and stochastically continuous MarkovFeller semigroup in continuous time, if there exists an ergodic measure whose support has a nonempty interior,then the e-property is satisfied on the interior of the support. In particular, it implies that, restricted on the support of each ergodic measure, the e-property and the eventual continuity are equivalent for the discrete-time and the stochastically continuous continuous-time Markov-Feller semigroups.展开更多
In this paper, we show that for an eventually strongly monotone skew-product semiflow τ, the strict ordering on Ec （the set consisting of continuous equilibria of τ） implies the strong one.
基金This work is supported by the National Natural Science Foundation of China (60474008)
文摘In this article, criteria of eventual stability are established for impulsive differential systems using piecewise continuous Lyapunov functions. The sufficient conditions that are obtained significantly depend on the moments of impulses. An example is discussed to illustrate the theorem.
文摘In this paper,we approximate the solution and also discuss the periodic behavior termed as eventual periodicity of solutions of(IBVPs)for some dispersive wave equations on a bounded domain corresponding to periodic forcing.The constructed numerical scheme is based on radial kernels and local in nature like finite difference method.The temporal variable is executed through RK4 scheme.Due to the local nature and sparse differentiation matrices our numerical scheme efficiently recovers the solution.The results achieved are validated and examined with other methods accessible in the literature.
文摘In this paper, we aim to find eventually vanished solutions, a special class of bounded solutions which tend to 0 as t → ±∞）, to a Lienard system with a time-dependent force. Since it is not a Hamiltonian system with small perturbations, the well-known Melnikov method is not applicable to the determination of the existence of eventually vanished solutions. We use a sequence of periodically forced systems to approximate the considered system, and find their periodic solutions. Difficulties caused by the non- Hamiltonian form are overcome by applying the Schauder＇s fixed point theorem. We show that the sequence of the periodic solutions has an accumulation giving an eventually vanished solution of the forced Lienard system.
文摘it In this paper, the properties of set-valued Eventual Supermartingle are discussed. The main result is that suppose {Fn, n ≥ 1） Lfc^1（X） be set-valued Eventual Supermartingle, ifsupE（d（0,Fτ）） 〈 ∞, then Fn →KF and SF^1≠φ, here T is the sets of all T bounded stopping times.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12061043,11661054,11261039)。
文摘The authors introduce the concepts of the eventual shadowing property and eventually shadowable point for set-valued dynamical systems and prove that a set-valued dynamical system has the eventual shadowing property if and only if every point in the phase space is eventually shadowable;every chain transitive set-valued dynamical system has either the eventual shadowing property or no eventually shadowable points;and a set-valued dynamical system admits an eventually shadowable point if and only if it admits a minimal eventually shadowable point.Moreover,it is proved that a set-valued dynamical system with the eventual shadowing property is chain mixing if and only if it is mixing and if and only if it has the specification property.
基金Supported by the National Natural Science Foundation of China(Grant No.12061043)。
文摘In this article,we provide some sufficient conditions for the dynamical systems with the eventual shadowing property to have positive topological entropy and several equivalent conditions for the dynamical systems with the eventual shadowing property to be mixing.
基金supported by the Comunidad de Madrid under Grant No.S2009/TIC-1692the Spanish MEC under Grant Nos.TIN2007-67353-C02-01 and TIN2008-06735-C02-01
文摘This paper considers the eventual leader election problem in asynchronous message-passing systems where an arbitrary number t of processes can crash（t〈n,where n is the total number of processes）.It considers weak assumptions both on the initial knowledge of the processes and on the network behavior.More precisely,initially,a process knows only its identity and the fact that the process identities are different and totally ordered（it knows neither n nor t）.Two eventual leader election protocols and a lower bound are presented.The first protocol assumes that a process also knows a lower bound α on the number of processes that do not crash.This protocol requires the following behavioral properties from the underlying network：the graph made up of the correct processes and fair lossy links is strongly connected,and there is a correct process connected to（n〈f）-α other correct processes（where f is the actual number of crashes in the considered run） through eventually timely paths（paths made up of correct processes and eventually timely links）.This protocol is not communication-efficient in the sense that each correct process has to send messages forever.The second protocol is communication-efficient：after some time,only the final common leader has to send messages forever.This protocol does not require the processes to know α,but requires stronger properties from the underlying network：each pair of correct processes has to be connected by fair lossy links（one in each direction）,and there is a correct process whose n〈f-1 output links to the rest of correct processes have to be eventually timely.A matching lower bound result shows that any eventual leader election protocol must have runs with this number of eventually timely links,even if all processes know all the processes identities.In addition to being communication-efficient,the second protocol has another noteworthy efficiency property,namely,be the run finite or infinite,all the local variables and message fields have a finite domain in the run.
基金This work was supported partly by the National High-tech Research and Development Program （863 Program） of China （2015AA01A202）, and partly by the National Natural Science Foundation of China （Grant Nos. 61370057 and 61421003）.
文摘Data items are usually replicated in modem dis- tributed data stores to obtain high performance and avail- ability. However, the availability-consistency and latency- consistency trade-offs exist in data replication, thus system designers intend to choose weak consistency models, such as eventual consistency, which may result in stale reads. Since stale data items may lead to serious application semantic problems, we consider how to increase the probability of data recency which provides a uniform view on recent versions of data items for all clients. In this work, we propose HARP, a framework that can enhance data recency of eventually con- sistent distributed data stores in an efficient and highly avail- able way. Through detecting possible stale reads under fail- ures or not, HARP can perform reread operations to elim- inate stale results only when needed based on our analysis on write/read processes. We also present solutions on how to deal with some practical anomalies in HARP, including de- layed, reordered and dropped messages and clock drift, and show how to extend HARP to multiple datacenters. Finally we implement HARP based on Cassandra, and the experi- ments show that HARP can effectively eliminate stale reads, with a low overhead （less than 6.9%） compared with original eventually consistent Cassandra.
基金supported by National Natural Science Foundation of China (No.11731009, No.12231002)Center for Statistical Science,Peking University。
文摘We investigate some relations between two kinds of semigroup regularities, namely the e-property and the eventual continuity, both of which contribute to the ergodicity for Markov processes on Polish spaces.More precisely, we prove that for Markov-Feller semigroup in discrete time and stochastically continuous MarkovFeller semigroup in continuous time, if there exists an ergodic measure whose support has a nonempty interior,then the e-property is satisfied on the interior of the support. In particular, it implies that, restricted on the support of each ergodic measure, the e-property and the eventual continuity are equivalent for the discrete-time and the stochastically continuous continuous-time Markov-Feller semigroups.
基金Partially supported by the National Basic Research Program of China,973 Project (No. 2005CB321902)the Key Lab of Random Complex Structures and Data Science,CAS
文摘In this paper, we show that for an eventually strongly monotone skew-product semiflow τ, the strict ordering on Ec （the set consisting of continuous equilibria of τ） implies the strong one.
