Suspension catalytic distillation (SCD) has been developed recently as an innovative technology in catalytic distillation. In this paper, a brief introduction to SCD is given and an equilibrium stage (EQ) modei is dev...Suspension catalytic distillation (SCD) has been developed recently as an innovative technology in catalytic distillation. In this paper, a brief introduction to SCD is given and an equilibrium stage (EQ) modei is developed to simulate this new process for synthesis of linear alkylbenzene (LAB) from benzene and 1-dodecene. Since non-ideality of this reaction systern is not strong, EQ modei developed could be applied to it successfully. Simulation results agree well with experimental data, and indicate some characteristics of SCD process as an advanced technology for the production of LAB: 100% conversion of olefins, low temperature (90-100℃) and low benzene/olefin mole ratio.展开更多
This paper deals with fishing models with stage structure and harvest in an inshore-offshore area. By using the monotonic theory and concave operators to functional differential equations and the qualitative theory of...This paper deals with fishing models with stage structure and harvest in an inshore-offshore area. By using the monotonic theory and concave operators to functional differential equations and the qualitative theory of differential equations, steady states of this dynamical systems representing fishery are derived, and their globally attracting behaviors are discussed. A brief biological meaning for the mathematical results is given.展开更多
In this paper, we propose and analyze a mathematical model to study the dynamics of a fishery resource system with stage structure in an aquatic environment that consists of two zones namely unreserved zone (fishing p...In this paper, we propose and analyze a mathematical model to study the dynamics of a fishery resource system with stage structure in an aquatic environment that consists of two zones namely unreserved zone (fishing permitted) and reserved zone (fishing is strictly prohibited). In this model we introduce a stage structure in which predators are split into two kinds as immature predators and mature predators. It is assumed that immature predators cannot catch the prey and their foods are given by their parents (mature predators). It is also assumed that the fishing of immature predators prohibited in the unreserved zone and predator species are not allowed to enter inside the reserved zone. The local and global stability analysis has been specified. Biological and Bionomical equilibriums of the system are derived. Mathematical formulation of the optimal harvesting policy is given and its solution is derived in the equilibrium case by using Pontryagin’s maximum principle.展开更多
In this paper,a two-stage model is developed to investigate the location strategy andthe commodity pricing strategy for a retail firm that wants to enter a spatial market with multiplecompetitive facilities,where a co...In this paper,a two-stage model is developed to investigate the location strategy andthe commodity pricing strategy for a retail firm that wants to enter a spatial market with multiplecompetitive facilities,where a competitor firm is already operating as a monopoly with several outlets.Expected market shares are calculated based on the stochastic customer behavior on networks.Theauthors provide a sufficient condition for the existence of equilibrium prices in the price game for thefirst time.The existence and uniqueness of the pure strategy Nash equilibrium price with a specifiedutility function are proved in the subgame.A metaheuristic based on tabu search is proposed tosearch the optimal location-price solution of the model.In addition,the authors provide two numericalexamples to illustrate how to obtain the optimal solution and conduct sensitivity analysis.The analysisshows that the best location decision is robust for the follower firm,price game is more intense whenincomes of consumers are lower or there are more substitution products,and neither chain retail gainsfrom the price competition.展开更多
A new improved tri-diagonal method was developed for the non-equilibrium stage model of the catalytic distillation by coupling consumptive reaction coefficient.The reactions in the distillation column were divided int...A new improved tri-diagonal method was developed for the non-equilibrium stage model of the catalytic distillation by coupling consumptive reaction coefficient.The reactions in the distillation column were divided into generative reaction and consumptive reac-tion.The non-equilibrium stage model was introduced for the catalytic distillation process of the dimethyl car-bonate(DMC)synthesis by urea methanolysis over solid based catalyst,and the improved tri-diagonal method was used to solve the model equations.Comparison of pre-dicted results with experiment data shows that the mean relative error of the yield of DMC was 3.78%under dif-ferent conditions such as different operating pressures and reaction temperatures.The improved tri-diagonal matrix method could avoid the negative values of the liquid com-positions during the calculations and restrain the fluc-tuation of compositions by slowing down the variations of the values in the iteration.The modeling results show that the improved tri-diagonal method was appropriate for system containing a wide range of boiling point com-ponents and a different rate of reactions.展开更多
基金Major State Basic Research Development Program(No.G2000048006)
文摘Suspension catalytic distillation (SCD) has been developed recently as an innovative technology in catalytic distillation. In this paper, a brief introduction to SCD is given and an equilibrium stage (EQ) modei is developed to simulate this new process for synthesis of linear alkylbenzene (LAB) from benzene and 1-dodecene. Since non-ideality of this reaction systern is not strong, EQ modei developed could be applied to it successfully. Simulation results agree well with experimental data, and indicate some characteristics of SCD process as an advanced technology for the production of LAB: 100% conversion of olefins, low temperature (90-100℃) and low benzene/olefin mole ratio.
基金This work is supported by the Special Fund for Major State Basic Research Projects (G1999032805) the National Natural Science Foundation of China (10171106).
文摘This paper deals with fishing models with stage structure and harvest in an inshore-offshore area. By using the monotonic theory and concave operators to functional differential equations and the qualitative theory of differential equations, steady states of this dynamical systems representing fishery are derived, and their globally attracting behaviors are discussed. A brief biological meaning for the mathematical results is given.
文摘In this paper, we propose and analyze a mathematical model to study the dynamics of a fishery resource system with stage structure in an aquatic environment that consists of two zones namely unreserved zone (fishing permitted) and reserved zone (fishing is strictly prohibited). In this model we introduce a stage structure in which predators are split into two kinds as immature predators and mature predators. It is assumed that immature predators cannot catch the prey and their foods are given by their parents (mature predators). It is also assumed that the fishing of immature predators prohibited in the unreserved zone and predator species are not allowed to enter inside the reserved zone. The local and global stability analysis has been specified. Biological and Bionomical equilibriums of the system are derived. Mathematical formulation of the optimal harvesting policy is given and its solution is derived in the equilibrium case by using Pontryagin’s maximum principle.
基金supported by the National Natural Science Foundation of China under Grant No. 70801003the Chinese Universities Scientific Fund (ZZ0915)
文摘In this paper,a two-stage model is developed to investigate the location strategy andthe commodity pricing strategy for a retail firm that wants to enter a spatial market with multiplecompetitive facilities,where a competitor firm is already operating as a monopoly with several outlets.Expected market shares are calculated based on the stochastic customer behavior on networks.Theauthors provide a sufficient condition for the existence of equilibrium prices in the price game for thefirst time.The existence and uniqueness of the pure strategy Nash equilibrium price with a specifiedutility function are proved in the subgame.A metaheuristic based on tabu search is proposed tosearch the optimal location-price solution of the model.In addition,the authors provide two numericalexamples to illustrate how to obtain the optimal solution and conduct sensitivity analysis.The analysisshows that the best location decision is robust for the follower firm,price game is more intense whenincomes of consumers are lower or there are more substitution products,and neither chain retail gainsfrom the price competition.
基金support from the National Science Key Foundation(Grant No.2006BAC02A08)was acknowledged.
文摘A new improved tri-diagonal method was developed for the non-equilibrium stage model of the catalytic distillation by coupling consumptive reaction coefficient.The reactions in the distillation column were divided into generative reaction and consumptive reac-tion.The non-equilibrium stage model was introduced for the catalytic distillation process of the dimethyl car-bonate(DMC)synthesis by urea methanolysis over solid based catalyst,and the improved tri-diagonal method was used to solve the model equations.Comparison of pre-dicted results with experiment data shows that the mean relative error of the yield of DMC was 3.78%under dif-ferent conditions such as different operating pressures and reaction temperatures.The improved tri-diagonal matrix method could avoid the negative values of the liquid com-positions during the calculations and restrain the fluc-tuation of compositions by slowing down the variations of the values in the iteration.The modeling results show that the improved tri-diagonal method was appropriate for system containing a wide range of boiling point com-ponents and a different rate of reactions.
