We study a random planar honeycomb lattice model, namely the random double hexagonal chains. This is a lattice system with nonperiodic boundary condition. The Wiener number is an important molecular descriptor based o...We study a random planar honeycomb lattice model, namely the random double hexagonal chains. This is a lattice system with nonperiodic boundary condition. The Wiener number is an important molecular descriptor based on the distances, which was introduced by the chemist Harold Wiener in 1947. By applying probabilistic method and combinatorial techniques we obtained an explicit analytical expression for the expected value of Wiener number of a random double hexagonal chain, and the limiting behaviors on the annealed entropy of Wiener number when the random double hexagonal chain becomes infinite in length are analyzed.展开更多
Some strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields （NSMC） on Cayley trees are studied. In the proof, a new technique for ...Some strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields （NSMC） on Cayley trees are studied. In the proof, a new technique for the study of strong limit theorems of Markov chains is extended to the case of Markov chain fields, The asymptotic equipartition properties with almost everywhere （a,e.） convergence for NSMC on Cayley trees are obtained,展开更多
This paper studies the strong law of large numbers and the Shannom-McMillan theorem for Markov chains field on Cayley tree. The authors first prove the strong law of large number on the frequencies of states and order...This paper studies the strong law of large numbers and the Shannom-McMillan theorem for Markov chains field on Cayley tree. The authors first prove the strong law of large number on the frequencies of states and orderd couples of states for Markov chains field on Cayley tree. Then they prove the Shannon-McMillan theorem with a.e. convergence for Markov chains field on Cayley tree. In the proof, a new technique in the study the strong limit theorem in probability theory is applied.展开更多
An algorithm is presented for estimating the expected number of customers for a class of Markovian queueing systems. The class is characterized by those systems whose transition matrix for the underlying customer arri...An algorithm is presented for estimating the expected number of customers for a class of Markovian queueing systems. The class is characterized by those systems whose transition matrix for the underlying customer arrival and departure process is finite, irreducible, and aperiodic. The algorithm does not depend on a closed-form solution for the limiting behavior of the queue. The expected number of customers is frequently used as a measure of effectiveness to describe the behavior of the system or to optimize its design or control. To calculate such a quantity one must usually obtain a closed-form expression for the steady-state probabilities. Unfortunately, of the myriad of Markovian queueing systems, only a few have known closed-form expressions for their steady-state probabilities. The most well-known, using Kendall’s notation, are the M/M/1 and the M/M/c system. The algorithm described below estimates the expected number in the system under steady-state without a need for closed form steady-state probabilities. All that is needed is the transition matrix for the underlying Markov chain.展开更多
In this paper, based on Cobb-Douglas production function, the structural stability of the supply chain system are analyzed by employing Lyapunov criteria. That the supply chain system structure, with the variance of t...In this paper, based on Cobb-Douglas production function, the structural stability of the supply chain system are analyzed by employing Lyapunov criteria. That the supply chain system structure, with the variance of the rate of re-production input funding, becomes unstable is proved. Noticeably, the solutions shows that when the optimal combination of input parameter element, the qualitative properties of supply chain system change and the supply chain system becomes unstable.展开更多
In a real world application supply chain, there are many elements of uncertainty such as supplier performance, market demands, product price, operation time, and shipping method which increases the difficulty for manu...In a real world application supply chain, there are many elements of uncertainty such as supplier performance, market demands, product price, operation time, and shipping method which increases the difficulty for manufacturers to quickly respond in order to fulfil the customer requirements. In this paper, the authors developed a fuzzy mathematical model to integrate different operational functions with the aim to provide satisfy decisions to help decision maker resolve production problem for all functions simultaneously. A triangular fuzzy number or possibilistic distribution represents all the uncertainty parameters. A comparison between a fuzzy model, a possibilistic model and a deterministic model is presented in this paper in order to distinguish the effectiveness of model in dealing the uncertain nature of supply chain. The proposed models performance is evaluated based on the operational aspect and computational aspect. The fuzzy model and the possibilistic model are expected to be more preferable to respond to the dynamic changes of the supply change network compared to the deterministic model. The developed fuzzy model seems to be more flexible in undertaking the lack of information or imprecise data of a variable in real situation whereas possibilistic model is more practical in solving an existing systems problem that has available data provided.展开更多
In a two-stage supply chain composed of one supplier and one retailer,the supply chain coordination mechanism in a fuzzy continuous demand environment is researched.A positive triangular fuzzy number is used to model ...In a two-stage supply chain composed of one supplier and one retailer,the supply chain coordination mechanism in a fuzzy continuous demand environment is researched.A positive triangular fuzzy number is used to model the external market demand.Using the method of fuzzy cut sets theory,both fuzzy decentralized and centralized decision-making processes are analyzed,and another model of fuzzy return contract is proposed to help coordinate such supply chain.It is shown that in fuzzy environment there exists a unique solution of the retailer＇s optimal order quantity,the double marginalization problem can be solved by providing different tactics for wholesale pricing and return pricing,and the fuzzy expected profit of each actor can be expected to improve in the return contract.Finally,a numerical example is given to illustrate the models and the solution-seeking process.展开更多
文摘We study a random planar honeycomb lattice model, namely the random double hexagonal chains. This is a lattice system with nonperiodic boundary condition. The Wiener number is an important molecular descriptor based on the distances, which was introduced by the chemist Harold Wiener in 1947. By applying probabilistic method and combinatorial techniques we obtained an explicit analytical expression for the expected value of Wiener number of a random double hexagonal chain, and the limiting behaviors on the annealed entropy of Wiener number when the random double hexagonal chain becomes infinite in length are analyzed.
基金Supported by National Basic Research Program of China(973 Program No.2007CBS14903)National Science Foundation of China(70671069)
文摘Some strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields （NSMC） on Cayley trees are studied. In the proof, a new technique for the study of strong limit theorems of Markov chains is extended to the case of Markov chain fields, The asymptotic equipartition properties with almost everywhere （a,e.） convergence for NSMC on Cayley trees are obtained,
文摘This paper studies the strong law of large numbers and the Shannom-McMillan theorem for Markov chains field on Cayley tree. The authors first prove the strong law of large number on the frequencies of states and orderd couples of states for Markov chains field on Cayley tree. Then they prove the Shannon-McMillan theorem with a.e. convergence for Markov chains field on Cayley tree. In the proof, a new technique in the study the strong limit theorem in probability theory is applied.
文摘An algorithm is presented for estimating the expected number of customers for a class of Markovian queueing systems. The class is characterized by those systems whose transition matrix for the underlying customer arrival and departure process is finite, irreducible, and aperiodic. The algorithm does not depend on a closed-form solution for the limiting behavior of the queue. The expected number of customers is frequently used as a measure of effectiveness to describe the behavior of the system or to optimize its design or control. To calculate such a quantity one must usually obtain a closed-form expression for the steady-state probabilities. Unfortunately, of the myriad of Markovian queueing systems, only a few have known closed-form expressions for their steady-state probabilities. The most well-known, using Kendall’s notation, are the M/M/1 and the M/M/c system. The algorithm described below estimates the expected number in the system under steady-state without a need for closed form steady-state probabilities. All that is needed is the transition matrix for the underlying Markov chain.
基金Supported by the National Excellent Youth Science Foundation of China (No.79725002)
文摘In this paper, based on Cobb-Douglas production function, the structural stability of the supply chain system are analyzed by employing Lyapunov criteria. That the supply chain system structure, with the variance of the rate of re-production input funding, becomes unstable is proved. Noticeably, the solutions shows that when the optimal combination of input parameter element, the qualitative properties of supply chain system change and the supply chain system becomes unstable.
文摘In a real world application supply chain, there are many elements of uncertainty such as supplier performance, market demands, product price, operation time, and shipping method which increases the difficulty for manufacturers to quickly respond in order to fulfil the customer requirements. In this paper, the authors developed a fuzzy mathematical model to integrate different operational functions with the aim to provide satisfy decisions to help decision maker resolve production problem for all functions simultaneously. A triangular fuzzy number or possibilistic distribution represents all the uncertainty parameters. A comparison between a fuzzy model, a possibilistic model and a deterministic model is presented in this paper in order to distinguish the effectiveness of model in dealing the uncertain nature of supply chain. The proposed models performance is evaluated based on the operational aspect and computational aspect. The fuzzy model and the possibilistic model are expected to be more preferable to respond to the dynamic changes of the supply change network compared to the deterministic model. The developed fuzzy model seems to be more flexible in undertaking the lack of information or imprecise data of a variable in real situation whereas possibilistic model is more practical in solving an existing systems problem that has available data provided.
基金Sponsored by the National Natural Science Foundation of China (7047106370771010)
文摘In a two-stage supply chain composed of one supplier and one retailer,the supply chain coordination mechanism in a fuzzy continuous demand environment is researched.A positive triangular fuzzy number is used to model the external market demand.Using the method of fuzzy cut sets theory,both fuzzy decentralized and centralized decision-making processes are analyzed,and another model of fuzzy return contract is proposed to help coordinate such supply chain.It is shown that in fuzzy environment there exists a unique solution of the retailer＇s optimal order quantity,the double marginalization problem can be solved by providing different tactics for wholesale pricing and return pricing,and the fuzzy expected profit of each actor can be expected to improve in the return contract.Finally,a numerical example is given to illustrate the models and the solution-seeking process.
