In this study,the authors consider an M/M/1 queuing system with attached inventory under an(s,S)control policy.The server takes multiple vacations whenever the inventory is depleted.It is assumed that the lead time an...In this study,the authors consider an M/M/1 queuing system with attached inventory under an(s,S)control policy.The server takes multiple vacations whenever the inventory is depleted.It is assumed that the lead time and the vacation time follow exponential distributions.The authors formulate the model as a quasi-birth-and-dearth(QBD)process and derive the stability condition of the system.Then,the stationary distribution in product form for the joint process of the queue length,the inventory level,and the server’s status is obtained.Furthermore,the conditional distributions of the inventory level when the server is on and operational,and when it is off due to a vacation,are derived.Using the stationary distribution,the authors obtain some performance measures of the system.The authors investigate analytically the effect of the server’s vacation on the performance measures.Finally,several numerical examples are presented to investigate the effects of some parameters on the performance measures,the optimal policy,and the optimal cost.展开更多
A mathematical model describing the dynamics of toxin producing phytoplankton- zooplankton interaction with instantaneous nutrient recycling is proposed. We have explored the dynamics of plankton ecosystem with multip...A mathematical model describing the dynamics of toxin producing phytoplankton- zooplankton interaction with instantaneous nutrient recycling is proposed. We have explored the dynamics of plankton ecosystem with multiple delays; one due to gestation period in the growth of phytoplankton population and second due to the delay in toxin liberated by TPP. It is established that a sequence of Hopf bifurcations occurs at the interior equilibrium as the delay increases through its critical value. The direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determined using the theory of normal form and center manifold. Meanwhile, effect of toxin on the stability of delayed plankton system is also established numerically. Finally, numerical simulations are carried out to support and supplement the analytical findings.展开更多
Acacia mangium Willd. and Acacia auriculiformis A. Cunn. ex. Benth. are two of the fast-growing tropical acacias which have received priority for genetic assessment and improvement. They were therefore proposed for ti...Acacia mangium Willd. and Acacia auriculiformis A. Cunn. ex. Benth. are two of the fast-growing tropical acacias which have received priority for genetic assessment and improvement. They were therefore proposed for timber production in a short rotation in Malaysia but were impeded by the multiple leaders (ML) formation which limited their value as sawn timber. This work attempts to investigate the causes of ML formation in four genotypes of A. mangium and A. auriculiformis as related to apical dominance, nutrition and plant growth hormones and their correlations. The effects of 6-benzylaminopurine and decapitation on ML formation of these genotypes were also investigated. 6-benzylaminopurine (BAP) as a foliar spray and also decapitation did not stimulate ML formation. However, they significantly increased the number of branches and reduced all other growth traits including height. However, basal diameter was not affected by decapitation. The effects of BAP increased consistently with increasing level of application. BAP at 1500 mg·Lǃ resulted in mortality of A. mangium provenances while A. auriculiformis provenances survived and grew normally. Some of the BAP treated plants of both species developed juvenile pinnate leaves. Decapitation of the apical bud resulted in the activation of the lateral bud immediately below the point of decapitation.展开更多
基金supported in part by the Natural Science Foundation of China under Grant No.71971189the Natural Science Foundation of Hebei Province under Grant No.A2019203313+1 种基金the Key Project of Scientific Research in Higher Education of Hebei Province of China under Grant No.ZD2018042in part by MEXT,Japan。
文摘In this study,the authors consider an M/M/1 queuing system with attached inventory under an(s,S)control policy.The server takes multiple vacations whenever the inventory is depleted.It is assumed that the lead time and the vacation time follow exponential distributions.The authors formulate the model as a quasi-birth-and-dearth(QBD)process and derive the stability condition of the system.Then,the stationary distribution in product form for the joint process of the queue length,the inventory level,and the server’s status is obtained.Furthermore,the conditional distributions of the inventory level when the server is on and operational,and when it is off due to a vacation,are derived.Using the stationary distribution,the authors obtain some performance measures of the system.The authors investigate analytically the effect of the server’s vacation on the performance measures.Finally,several numerical examples are presented to investigate the effects of some parameters on the performance measures,the optimal policy,and the optimal cost.
文摘A mathematical model describing the dynamics of toxin producing phytoplankton- zooplankton interaction with instantaneous nutrient recycling is proposed. We have explored the dynamics of plankton ecosystem with multiple delays; one due to gestation period in the growth of phytoplankton population and second due to the delay in toxin liberated by TPP. It is established that a sequence of Hopf bifurcations occurs at the interior equilibrium as the delay increases through its critical value. The direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determined using the theory of normal form and center manifold. Meanwhile, effect of toxin on the stability of delayed plankton system is also established numerically. Finally, numerical simulations are carried out to support and supplement the analytical findings.
文摘Acacia mangium Willd. and Acacia auriculiformis A. Cunn. ex. Benth. are two of the fast-growing tropical acacias which have received priority for genetic assessment and improvement. They were therefore proposed for timber production in a short rotation in Malaysia but were impeded by the multiple leaders (ML) formation which limited their value as sawn timber. This work attempts to investigate the causes of ML formation in four genotypes of A. mangium and A. auriculiformis as related to apical dominance, nutrition and plant growth hormones and their correlations. The effects of 6-benzylaminopurine and decapitation on ML formation of these genotypes were also investigated. 6-benzylaminopurine (BAP) as a foliar spray and also decapitation did not stimulate ML formation. However, they significantly increased the number of branches and reduced all other growth traits including height. However, basal diameter was not affected by decapitation. The effects of BAP increased consistently with increasing level of application. BAP at 1500 mg·Lǃ resulted in mortality of A. mangium provenances while A. auriculiformis provenances survived and grew normally. Some of the BAP treated plants of both species developed juvenile pinnate leaves. Decapitation of the apical bud resulted in the activation of the lateral bud immediately below the point of decapitation.
