In this paper, the authors discuss the relationship in detail between the rank of M in the modified matrix M = A ＋ BC^＊ and the rank of matrix A. The authors do believe the results are useful tools in the modified m...In this paper, the authors discuss the relationship in detail between the rank of M in the modified matrix M = A ＋ BC^＊ and the rank of matrix A. The authors do believe the results are useful tools in the modified matrices.展开更多
The aim of this paper is to prove the well-posedness（existence and uniqueness） of the L p entropy solution to the homogeneous Dirichlet problems for the anisotropic degenerate parabolic-hyperbolic equations with L p...The aim of this paper is to prove the well-posedness（existence and uniqueness） of the L p entropy solution to the homogeneous Dirichlet problems for the anisotropic degenerate parabolic-hyperbolic equations with L p initial value.We use the device of doubling variables and some technical analysis to prove the uniqueness result.Moreover we can prove that the L p entropy solution can be obtained as the limit of solutions of the corresponding regularized equations of nondegenerate parabolic type.展开更多
Abstract This paper deals with a discrete-time batch arrival retrial queue with the server subject to starting failures.Diferent from standard batch arrival retrial queues with starting failures,we assume that each cu...Abstract This paper deals with a discrete-time batch arrival retrial queue with the server subject to starting failures.Diferent from standard batch arrival retrial queues with starting failures,we assume that each customer after service either immediately returns to the orbit for another service with probabilityθor leaves the system forever with probability 1θ（0≤θ〈1）.On the other hand,if the server is started unsuccessfully by a customer（external or repeated）,the server is sent to repair immediately and the customer either joins the orbit with probability q or leaves the system forever with probability 1 q（0≤q〈1）.Firstly,we introduce an embedded Markov chain and obtain the necessary and sufcient condition for ergodicity of this embedded Markov chain.Secondly,we derive the steady-state joint distribution of the server state and the number of customers in the system/orbit at arbitrary time.We also derive a stochastic decomposition law.In the special case of individual arrivals,we develop recursive formulae for calculating the steady-state distribution of the orbit size.Besides,we investigate the relation between our discrete-time system and its continuous counterpart.Finally,some numerical examples show the influence of the parameters on the mean orbit size.展开更多
This paper deals with the pos/neg-weighted p-median problem on tree graphs where all customers are modeled as subtrees. We present a polynomial algorithm for the 2-median problem on an arbitrary tree. Then we improve ...This paper deals with the pos/neg-weighted p-median problem on tree graphs where all customers are modeled as subtrees. We present a polynomial algorithm for the 2-median problem on an arbitrary tree. Then we improve the time complexity to O（n logn） for the problem on a balanced tree, where n is the number of the vertices in the tree.展开更多
基金the National Natural Sciences Foundation of China(10371044)the Science and Technology Commission of Shanghai Municipality through Grant(04JC14031)+1 种基金the University Young Teacher Sciences Foundation of Anhui Province(2006jq1220zd)Supported by the Ph.D.,Program Scholarship Fund of ECNU(2007)
文摘In this paper, the authors discuss the relationship in detail between the rank of M in the modified matrix M = A ＋ BC^＊ and the rank of matrix A. The authors do believe the results are useful tools in the modified matrices.
基金Yachun Li’s research was supported partly by National Natural Science Foundation of China (10571120,10971135)the Program for New Century Excellent Talents of Chinese Ministry of Education (NCET-07-0546)+3 种基金Shanghai Shuguang Project 06SG11Zhigang Wang’s research was supported partly by Shanghai Jiao Tong University Innovation Fund For Postgraduates (AE071202)the University Young Teacher Sciences Foundation of Anhui Province (2010SQRL145)the Quality Project Found of Fuyang Normal College (2010JPKC07)
文摘The aim of this paper is to prove the well-posedness（existence and uniqueness） of the L p entropy solution to the homogeneous Dirichlet problems for the anisotropic degenerate parabolic-hyperbolic equations with L p initial value.We use the device of doubling variables and some technical analysis to prove the uniqueness result.Moreover we can prove that the L p entropy solution can be obtained as the limit of solutions of the corresponding regularized equations of nondegenerate parabolic type.
基金Supported by the National Natural Science Foundation of China(Nos.11171019,11171179,and 11271373)Program for New Century Excellent Talents in University(No.NCET-11-0568)+2 种基金the Fundamental Research Funds for the Central Universities(No.2011JBZ012)Tianyuan Fund for Mathematics(Nos.11226200 and 11226251)Program for Science Research of Fuyang Normal College(2013FSKJ01ZD)
文摘Abstract This paper deals with a discrete-time batch arrival retrial queue with the server subject to starting failures.Diferent from standard batch arrival retrial queues with starting failures,we assume that each customer after service either immediately returns to the orbit for another service with probabilityθor leaves the system forever with probability 1θ（0≤θ〈1）.On the other hand,if the server is started unsuccessfully by a customer（external or repeated）,the server is sent to repair immediately and the customer either joins the orbit with probability q or leaves the system forever with probability 1 q（0≤q〈1）.Firstly,we introduce an embedded Markov chain and obtain the necessary and sufcient condition for ergodicity of this embedded Markov chain.Secondly,we derive the steady-state joint distribution of the server state and the number of customers in the system/orbit at arbitrary time.We also derive a stochastic decomposition law.In the special case of individual arrivals,we develop recursive formulae for calculating the steady-state distribution of the orbit size.Besides,we investigate the relation between our discrete-time system and its continuous counterpart.Finally,some numerical examples show the influence of the parameters on the mean orbit size.
基金Supported by the National Nature Science Foundation of China(Nos.11471210,11571222)
文摘This paper deals with the pos/neg-weighted p-median problem on tree graphs where all customers are modeled as subtrees. We present a polynomial algorithm for the 2-median problem on an arbitrary tree. Then we improve the time complexity to O（n logn） for the problem on a balanced tree, where n is the number of the vertices in the tree.
