A -4/3|log |-2 result is obtained for the existence time of solutions of semi- linear different speed Klein-Gordon system in one space dimension for weakly decaying Cauchy data, of size , in certain circumstances of ...A -4/3|log |-2 result is obtained for the existence time of solutions of semi- linear different speed Klein-Gordon system in one space dimension for weakly decaying Cauchy data, of size , in certain circumstances of nonlinearity.展开更多
Based on the methods introduced by Klainerman and Ponce, and Cohn, a lower bounded estimate of the existence time for a kind of semilinear Schrdinger equation is obtained in this paper. The implementation of this meth...Based on the methods introduced by Klainerman and Ponce, and Cohn, a lower bounded estimate of the existence time for a kind of semilinear Schrdinger equation is obtained in this paper. The implementation of this method depends on the L p-L q estimate and the energy estimate.展开更多
In this paper we discuss the discrete, time non--homogeneous discounted Markovian decisionprogramming, where the state space and all action sets are countable. Suppose that the optimumvalue function is finite. We give...In this paper we discuss the discrete, time non--homogeneous discounted Markovian decisionprogramming, where the state space and all action sets are countable. Suppose that the optimumvalue function is finite. We give the necessary and sufficient conditions for the existence of anoptimal policy. Suppose that the absolute mean of rewards is relatively bounded. We also give thenecessary and sufficient conditions for the existence of an optimal policy.展开更多
In this paper,the mean curvature flow of complete submanifolds in Euclidean space with convex Gauss image and bounded curvature is studied.The confinable property of the Gauss image under the mean curvature flow is pr...In this paper,the mean curvature flow of complete submanifolds in Euclidean space with convex Gauss image and bounded curvature is studied.The confinable property of the Gauss image under the mean curvature flow is proved,which in turn helps one to obtain the curvature estimates.Then the author proves a long time existence result.The asymptotic behavior of these solutions when t→∞is also studied.展开更多
Distributed network architecture and dynamic change of nodes makes the operation of structured peer-to-peer networks unpredictable. This article aims to present a research on the running rule of structured peer-to-pee...Distributed network architecture and dynamic change of nodes makes the operation of structured peer-to-peer networks unpredictable. This article aims to present a research on the running rule of structured peer-to-peer networks through a mathematical model. The proposed model provides a low-complexity means to estimate the performance of a structured peer-to-peer network from two aspects： the average existent time of a node and probability of returning to a temporarily steady state of network. On the basis of the results, it can be concluded that the proposed structured peer-to-peer network is suitable for those conditions where the frequency of node change is under limited value, and this value mainly depends on the initializing time of the node. Otherwise, structured peer-to-peer network can be abstracted as a network queuing system, which is composed of many node queuing systems in a meshy way and the relation between the throughput of the node system and network system is analyzed.展开更多
In this paper we study the local or global(in time)existence of small data solutions to semi-linear fractionalσ-evolution equations with nonlinear memory.Our main goals is to explain on the one hand the influence of ...In this paper we study the local or global(in time)existence of small data solutions to semi-linear fractionalσ-evolution equations with nonlinear memory.Our main goals is to explain on the one hand the influence of the memory term and on the other hand the influence of higher regularity of the data on qualitative properties of solutions.展开更多
In this paper,we study the star-shaped hypersurfaces evolved by a class of inverse mean curvature type flows in the anti-de Sitter-Schwarzschild manifold.We give C^(0),C^(1),C^(2) estimates of the flow.Using these fac...In this paper,we study the star-shaped hypersurfaces evolved by a class of inverse mean curvature type flows in the anti-de Sitter-Schwarzschild manifold.We give C^(0),C^(1),C^(2) estimates of the flow.Using these facts,we prove that the solution exists for all time and the principal curvatures converge to 1 polynomially fast.展开更多
Assume M is a closed 3-manifold whose universal covering is not S^3.We show that the obstruction to extend the Ricci flow is the boundedness L 3/2-norm of the scalar curvature R(t),i.e.,the Ricci flow can be extended ...Assume M is a closed 3-manifold whose universal covering is not S^3.We show that the obstruction to extend the Ricci flow is the boundedness L 3/2-norm of the scalar curvature R(t),i.e.,the Ricci flow can be extended over finite time T if and only if the||R(t)||L 3/2 is uniformly bounded for 0≤t<T.On the other hand,if the fundamental group of M is finite and the||R(t)||L 3/2 is bounded for all time under the Ricci flow,then M is diffeomorphic to a 3-dimensional spherical space-form.展开更多
文摘A -4/3|log |-2 result is obtained for the existence time of solutions of semi- linear different speed Klein-Gordon system in one space dimension for weakly decaying Cauchy data, of size , in certain circumstances of nonlinearity.
文摘Based on the methods introduced by Klainerman and Ponce, and Cohn, a lower bounded estimate of the existence time for a kind of semilinear Schrdinger equation is obtained in this paper. The implementation of this method depends on the L p-L q estimate and the energy estimate.
文摘In this paper we discuss the discrete, time non--homogeneous discounted Markovian decisionprogramming, where the state space and all action sets are countable. Suppose that the optimumvalue function is finite. We give the necessary and sufficient conditions for the existence of anoptimal policy. Suppose that the absolute mean of rewards is relatively bounded. We also give thenecessary and sufficient conditions for the existence of an optimal policy.
基金the National Natural Science Foundation of China(No.10531090).
文摘In this paper,the mean curvature flow of complete submanifolds in Euclidean space with convex Gauss image and bounded curvature is studied.The confinable property of the Gauss image under the mean curvature flow is proved,which in turn helps one to obtain the curvature estimates.Then the author proves a long time existence result.The asymptotic behavior of these solutions when t→∞is also studied.
文摘Distributed network architecture and dynamic change of nodes makes the operation of structured peer-to-peer networks unpredictable. This article aims to present a research on the running rule of structured peer-to-peer networks through a mathematical model. The proposed model provides a low-complexity means to estimate the performance of a structured peer-to-peer network from two aspects： the average existent time of a node and probability of returning to a temporarily steady state of network. On the basis of the results, it can be concluded that the proposed structured peer-to-peer network is suitable for those conditions where the frequency of node change is under limited value, and this value mainly depends on the initializing time of the node. Otherwise, structured peer-to-peer network can be abstracted as a network queuing system, which is composed of many node queuing systems in a meshy way and the relation between the throughput of the node system and network system is analyzed.
基金The research of this article is supported by the DAAD,Erasmus+Project between the Hassiba Benbouali University of Chlef(Algeria)and TU Bergakademie Freiberg,2015-1-DE01-KA107-002026
文摘In this paper we study the local or global(in time)existence of small data solutions to semi-linear fractionalσ-evolution equations with nonlinear memory.Our main goals is to explain on the one hand the influence of the memory term and on the other hand the influence of higher regularity of the data on qualitative properties of solutions.
基金supported by National Natural Science Foundation of China(Grant No.11831005)a collaboration project funded by National Natural Science Foundation of China and the Research Foundation Flanders(Grant No.11961131001)。
文摘In this paper,we study the star-shaped hypersurfaces evolved by a class of inverse mean curvature type flows in the anti-de Sitter-Schwarzschild manifold.We give C^(0),C^(1),C^(2) estimates of the flow.Using these facts,we prove that the solution exists for all time and the principal curvatures converge to 1 polynomially fast.
基金The author would like to express his gratitude to X.Chen who brought this problem to his attention and provided many helpful and stimulating discussions.He is very grateful of V.Apostolov’s detailed suggestions for this paper.He also would like to thank H.Li for discussing and reviewing the paper and R.Haslhofer for useful comments.
文摘Assume M is a closed 3-manifold whose universal covering is not S^3.We show that the obstruction to extend the Ricci flow is the boundedness L 3/2-norm of the scalar curvature R(t),i.e.,the Ricci flow can be extended over finite time T if and only if the||R(t)||L 3/2 is uniformly bounded for 0≤t<T.On the other hand,if the fundamental group of M is finite and the||R(t)||L 3/2 is bounded for all time under the Ricci flow,then M is diffeomorphic to a 3-dimensional spherical space-form.
