A new method of the design and machining the casting moulds of helical intake ports of diesel engines is presented based on CAD / CAM technique. The problems about the smooth continuity between patches, the cutter int...A new method of the design and machining the casting moulds of helical intake ports of diesel engines is presented based on CAD / CAM technique. The problems about the smooth continuity between patches, the cutter interference and the determination of the mould split curve are discussed in details.The CAGD system of the intake port has been developed. and the casting mould is machined sucessfully on NC machine.展开更多
In this paper,we consider a tuberculosis model with incomplete treatment and extend the model to a Caputo fractional-order and two-patch version with exogenous re-infection among the treated individuals,in which only ...In this paper,we consider a tuberculosis model with incomplete treatment and extend the model to a Caputo fractional-order and two-patch version with exogenous re-infection among the treated individuals,in which only susceptible individuals can travel freely between the patches.The model has multiple equilibria.We determine conditions that lead to the appearance of a backward bifurcation.The results show that the TB model can have exogenous reinfection among the treated individuals and,at the same time,does not exhibit backward bifurcation.Also,conditions that lead to the global asymptotic stability of the disease-free equilibrium are obtained.In case without reinfection,the model has four equilibria.In this case,the global asymptotic stability of the equilibria is established using the Lyapunov function theory together with the LaSalle invariance principle for fractional differential equations(FDEs).Numerical simulations confirm the validity of the theoretical results.展开更多
In this paper,we propose a fractional-order and two-patch model of tuberculosis(TB)epidemic,in which susceptible,slow latent,fast latent and infectious individuals can travel freely between the patches,but not under t...In this paper,we propose a fractional-order and two-patch model of tuberculosis(TB)epidemic,in which susceptible,slow latent,fast latent and infectious individuals can travel freely between the patches,but not under treatment infected individuals,due to medical reasons.We obtain the basic reproduction number Ro for the model and extend the classical LaSalle's invariance principle for fractional differential equations.We show that if R0<1,the disease-free equilibrium(DFE)is locally and globally asymptotically stable.If Ro>l,we obtain sufficient conditions under which the endernic equilibrium is unique and globally asymptotically stable.We extend the model by inclusion the time-dependent controls(effective treatment controls in both patches and controls of screening on travel of infectious individuals between patches),and formulate a fractional optimal control problem to reduce the spread of the disease.The numerical results show that the use of all controls has the most impact on disease control,and decreases the size of all infected compartments,but increases the size of susceptible compartment in both patches.We,also,investigate the impact of the fractional derivative order a on the values of the controls(0.7≤α≤1).The results show that the maximum levels of effective treatment controls in both patches increase when a is reduced from l,while the maximum level of the travel screening control of infectious individuals from patch 2 to patch 1 increases when o limits to 1.展开更多
文摘A new method of the design and machining the casting moulds of helical intake ports of diesel engines is presented based on CAD / CAM technique. The problems about the smooth continuity between patches, the cutter interference and the determination of the mould split curve are discussed in details.The CAGD system of the intake port has been developed. and the casting mould is machined sucessfully on NC machine.
文摘In this paper,we consider a tuberculosis model with incomplete treatment and extend the model to a Caputo fractional-order and two-patch version with exogenous re-infection among the treated individuals,in which only susceptible individuals can travel freely between the patches.The model has multiple equilibria.We determine conditions that lead to the appearance of a backward bifurcation.The results show that the TB model can have exogenous reinfection among the treated individuals and,at the same time,does not exhibit backward bifurcation.Also,conditions that lead to the global asymptotic stability of the disease-free equilibrium are obtained.In case without reinfection,the model has four equilibria.In this case,the global asymptotic stability of the equilibria is established using the Lyapunov function theory together with the LaSalle invariance principle for fractional differential equations(FDEs).Numerical simulations confirm the validity of the theoretical results.
文摘In this paper,we propose a fractional-order and two-patch model of tuberculosis(TB)epidemic,in which susceptible,slow latent,fast latent and infectious individuals can travel freely between the patches,but not under treatment infected individuals,due to medical reasons.We obtain the basic reproduction number Ro for the model and extend the classical LaSalle's invariance principle for fractional differential equations.We show that if R0<1,the disease-free equilibrium(DFE)is locally and globally asymptotically stable.If Ro>l,we obtain sufficient conditions under which the endernic equilibrium is unique and globally asymptotically stable.We extend the model by inclusion the time-dependent controls(effective treatment controls in both patches and controls of screening on travel of infectious individuals between patches),and formulate a fractional optimal control problem to reduce the spread of the disease.The numerical results show that the use of all controls has the most impact on disease control,and decreases the size of all infected compartments,but increases the size of susceptible compartment in both patches.We,also,investigate the impact of the fractional derivative order a on the values of the controls(0.7≤α≤1).The results show that the maximum levels of effective treatment controls in both patches increase when a is reduced from l,while the maximum level of the travel screening control of infectious individuals from patch 2 to patch 1 increases when o limits to 1.
