Several factors influence bus transit reliability which includes bus stop conditions along the route, traffic conditions, route of travel and time of day. The overall transit bus reli- ability is generally affected by...Several factors influence bus transit reliability which includes bus stop conditions along the route, traffic conditions, route of travel and time of day. The overall transit bus reli- ability is generally affected by dwell time （DT）, the fare payment method, the bus stop location, and the number of passengers alighting or boarding. A new variable is defined in this study, total bus stop time （TBST）, which is the summation of DT and the time it takes a bus to effectively park at a bus stop and the re-entering the traffic stream. It is suggested that the overall bus transit reliability along routes could be improved if the TBST is mini- mized at bus stops. In this study, TBST models for bus stops located at mid-blocks and near intersections were developed based on multivariate regression analysis using ordinary least squares method. Data collection was conducted at 60 bus stops, 30 of which were near intersections and 30 at mid-blocks, in Washington DC during morning, mid-day and evening peak hours. The variables observed at each bus stop are as follows： number of passengers alighting or boarding, DT, TBST, bus stop type, bus pad, length number of lanes on approach to the bus stop, and permitted parking. Statistical inferences were based on 5% level of significance. From the results, it was inferred that the new variable, TBST, could potentially be used to improve scheduling and transit bus systems planning in a dense urban area.展开更多
Based on literature [J. Q. Li, Z. E. Ma and F. Q. Zhang, Stability analysis for an epidemic model with stage structure, J. Appl. Math. Comput. 9 （2008） 1672-1679], incorporating the recovery of the infected populati...Based on literature [J. Q. Li, Z. E. Ma and F. Q. Zhang, Stability analysis for an epidemic model with stage structure, J. Appl. Math. Comput. 9 （2008） 1672-1679], incorporating the recovery of the infected population with the length of the infectious periods, a modified epidemic disease SIS model with delay and stage was investigated. First, the criteria keeping stability with delay were given. Next, in order to lower the level of the infected individuals and minimize the cost of treatment, mixed, early and late therapeutic strategies were introduced into our model, respectively. Then we investigated the existence and uniqueness of optimal controls. And then, we expressed the unique optimal control in terms of the solution of the optimality systems. Finally, by numerical simulations, several important results were acquired： （1） The terminal time influenced the early optimal control largely. In detail, for a shorter terminal time it was optimal to initiate treatment with maximal effort at the start of the epidemic and continue treatment with maximal effort until the switch time was arrived. But for a longer terminal time, the maximal treatment effort need not be a prerequisite at the start or end of the epidemic but it was obligatory at the metaphase of the epidemic. （2） For our SIS model, minimizing the total infectious burden of the disease can be achieved by only early optimal treatment tactics. （3） For a disease with a shorter infectious period time,more cost would be spent to control the disease in order to achieve the optimal control objective. Otherwise, a relative lower cost would be to control the disease with a longer infectious period.展开更多
The goal of this paper is to investigate different reconstruction methods for solving the limited angle problem in reconstructing the projection data from a stationary multi-pinhole system based on a three-head clinic...The goal of this paper is to investigate different reconstruction methods for solving the limited angle problem in reconstructing the projection data from a stationary multi-pinhole system based on a three-head clinical single photon emission computed tomography （SPECT） camera. Three iterative recon- struction approaches were studied including maximum likelihood expectation maximization （MLEM）, maximum a posteriori expectation maximization （MAPEM） with a smoothing prior, and an alternating optimization schemes from MLEM and total variation （TV） optimization. A three-headed multipinhole SPECT was simulated with apertures of nine 1-mm pinholes each, and covered scanning volume of 6-mm diameter. The reconstructions were optimized for various iterations based on visual inspections, and finally 20 iterations were applied for each method. For both MLEM-TV and MAPEM-TV, various initial reconstructions before TV optimization were studied. The smoothing parameter for MAPEM and the gradient descent constant for TV were also investigated through visual comparison. The preliminary results showed the 3 reconstruction methods generated compatible images, and can restore the images from projection data suffering limited angular sampling. However, MLEM was noisy for low-count and highly limited angle data, and thus suitable smoothing in MAPEM alleviated this problem, initial reconstructions were necessary for better edge enhancement in TV. The conclusion is that TV might be potential in producing more edge-enhanced images if all parameters were optimized.展开更多
The flow of Ree–Eyring and Casson non-Newtonian fluids is investigated using a variational principle to optimize the total stress.The variationally obtained solutions are compared to the analytical solutions derived ...The flow of Ree–Eyring and Casson non-Newtonian fluids is investigated using a variational principle to optimize the total stress.The variationally obtained solutions are compared to the analytical solutions derived from the Weissenberg–Rabinowitsch–Mooney equation and the results are found to be identical within acceptable numerical errors and modeling approximations.展开更多
文摘Several factors influence bus transit reliability which includes bus stop conditions along the route, traffic conditions, route of travel and time of day. The overall transit bus reli- ability is generally affected by dwell time （DT）, the fare payment method, the bus stop location, and the number of passengers alighting or boarding. A new variable is defined in this study, total bus stop time （TBST）, which is the summation of DT and the time it takes a bus to effectively park at a bus stop and the re-entering the traffic stream. It is suggested that the overall bus transit reliability along routes could be improved if the TBST is mini- mized at bus stops. In this study, TBST models for bus stops located at mid-blocks and near intersections were developed based on multivariate regression analysis using ordinary least squares method. Data collection was conducted at 60 bus stops, 30 of which were near intersections and 30 at mid-blocks, in Washington DC during morning, mid-day and evening peak hours. The variables observed at each bus stop are as follows： number of passengers alighting or boarding, DT, TBST, bus stop type, bus pad, length number of lanes on approach to the bus stop, and permitted parking. Statistical inferences were based on 5% level of significance. From the results, it was inferred that the new variable, TBST, could potentially be used to improve scheduling and transit bus systems planning in a dense urban area.
基金Acknowledgments The authors would like to thank the editor and the referee for constructive comments which significantly improves this paper. In addition, this work was supported by the National Natural Science Foundation of China （No. 11471243）.
文摘Based on literature [J. Q. Li, Z. E. Ma and F. Q. Zhang, Stability analysis for an epidemic model with stage structure, J. Appl. Math. Comput. 9 （2008） 1672-1679], incorporating the recovery of the infected population with the length of the infectious periods, a modified epidemic disease SIS model with delay and stage was investigated. First, the criteria keeping stability with delay were given. Next, in order to lower the level of the infected individuals and minimize the cost of treatment, mixed, early and late therapeutic strategies were introduced into our model, respectively. Then we investigated the existence and uniqueness of optimal controls. And then, we expressed the unique optimal control in terms of the solution of the optimality systems. Finally, by numerical simulations, several important results were acquired： （1） The terminal time influenced the early optimal control largely. In detail, for a shorter terminal time it was optimal to initiate treatment with maximal effort at the start of the epidemic and continue treatment with maximal effort until the switch time was arrived. But for a longer terminal time, the maximal treatment effort need not be a prerequisite at the start or end of the epidemic but it was obligatory at the metaphase of the epidemic. （2） For our SIS model, minimizing the total infectious burden of the disease can be achieved by only early optimal treatment tactics. （3） For a disease with a shorter infectious period time,more cost would be spent to control the disease in order to achieve the optimal control objective. Otherwise, a relative lower cost would be to control the disease with a longer infectious period.
基金Supported by the NSC (No.97-2314-B-182-029-MY3)the Research Fund of Chang Gung Memorial Hospital (No.CMRPD34005)
文摘The goal of this paper is to investigate different reconstruction methods for solving the limited angle problem in reconstructing the projection data from a stationary multi-pinhole system based on a three-head clinical single photon emission computed tomography （SPECT） camera. Three iterative recon- struction approaches were studied including maximum likelihood expectation maximization （MLEM）, maximum a posteriori expectation maximization （MAPEM） with a smoothing prior, and an alternating optimization schemes from MLEM and total variation （TV） optimization. A three-headed multipinhole SPECT was simulated with apertures of nine 1-mm pinholes each, and covered scanning volume of 6-mm diameter. The reconstructions were optimized for various iterations based on visual inspections, and finally 20 iterations were applied for each method. For both MLEM-TV and MAPEM-TV, various initial reconstructions before TV optimization were studied. The smoothing parameter for MAPEM and the gradient descent constant for TV were also investigated through visual comparison. The preliminary results showed the 3 reconstruction methods generated compatible images, and can restore the images from projection data suffering limited angular sampling. However, MLEM was noisy for low-count and highly limited angle data, and thus suitable smoothing in MAPEM alleviated this problem, initial reconstructions were necessary for better edge enhancement in TV. The conclusion is that TV might be potential in producing more edge-enhanced images if all parameters were optimized.
文摘The flow of Ree–Eyring and Casson non-Newtonian fluids is investigated using a variational principle to optimize the total stress.The variationally obtained solutions are compared to the analytical solutions derived from the Weissenberg–Rabinowitsch–Mooney equation and the results are found to be identical within acceptable numerical errors and modeling approximations.
