The age of infection approach introduced by Kermack and Mckendrick in 1927 gives a unified way of describing and analyzing a variety of epidemic models, including models with multiple stages, treatment, and heterogene...The age of infection approach introduced by Kermack and Mckendrick in 1927 gives a unified way of describing and analyzing a variety of epidemic models, including models with multiple stages, treatment, and heterogeneous mixing. The author gives a description of the main results for such models, emphasizing the use of the final size relation to estimate the size of the epidemic.展开更多
The wetted perimeter method(WPM) is used in hydrology and hydraulics to calculate instream flows.The WPM requires few data.It requires only the values of the wetted perimeter,flow and water level,which can be obtained...The wetted perimeter method(WPM) is used in hydrology and hydraulics to calculate instream flows.The WPM requires few data.It requires only the values of the wetted perimeter,flow and water level,which can be obtained from the hydrologic stations of the river in question.In addition,the WPM is not limited by the impacts of human activities on the river runoff.Therefore,this method is generally suitable for the current conditions in China.However,the process of applying the WPM involves two key aspects:how to plot the curve describing the relationship between the wetted perimeter and the discharge and how to confirm the breakpoint of the wetted perimeter-discharge curve.The traditional method is to calculate the curvature or the slope of the wetted perimeter-discharge curve to obtain the minimum flow.According to this method,the minimum flow corresponds to the point of maximum curvature or to the point at which the slope of the curve is equal to 1.The wetted perimeter-discharge curve of a natural river is only part of the complete curve.Thus,the instream flow calculated by the traditional method is the minimum or maximum discharge.The new criterion for defining the breakpoint of the wetted perimeter-discharge curve is that the slope at the breakpoint is a relative maximum,the second-largest slope.The discharges at the breakpoints corresponded to the minimum flow levels required to maintain the ecological function of the river.The minimum instream flow requirements(MIFRs) of four typical reaches,Zhuba,Daofu,Ganzi and Zumuzu hydrological stations on the West Course of the First Stage Project of the South-North Water Transfer Project(WCFSPSNWTP),are calculated using an improved wetted perimeter method(IWPM).The results show that the MIFRs of Zhuba,Daofu,Ganzi and Zumuzu are approximately 9.06-14.5 m 3 s-1,20.7-43.5 m3 s-1,38.8-77.2 m 3 s-1 and 40.4-59.5 m 3 s-1,corresponding to 11.7%-33.9%,14.2%-37.6%,12.4%-28.4% and 17.5%-30.2%,respectively of the annual average flow(AAF).These MIFRs can maintain good ecological function in a river according to the criterion furnished by the Tennant method.展开更多
文摘The age of infection approach introduced by Kermack and Mckendrick in 1927 gives a unified way of describing and analyzing a variety of epidemic models, including models with multiple stages, treatment, and heterogeneous mixing. The author gives a description of the main results for such models, emphasizing the use of the final size relation to estimate the size of the epidemic.
基金supported by the National Natural Science Foundation of China (Grant No. 50809027)the Fundamental Research Funds for the Central Universities (Grant No. 11MG15)the Open Research Fund Program of State Key Laboratory of Water Resources and Hydropower Engineering Science (Grant No. 2009B050)
文摘The wetted perimeter method(WPM) is used in hydrology and hydraulics to calculate instream flows.The WPM requires few data.It requires only the values of the wetted perimeter,flow and water level,which can be obtained from the hydrologic stations of the river in question.In addition,the WPM is not limited by the impacts of human activities on the river runoff.Therefore,this method is generally suitable for the current conditions in China.However,the process of applying the WPM involves two key aspects:how to plot the curve describing the relationship between the wetted perimeter and the discharge and how to confirm the breakpoint of the wetted perimeter-discharge curve.The traditional method is to calculate the curvature or the slope of the wetted perimeter-discharge curve to obtain the minimum flow.According to this method,the minimum flow corresponds to the point of maximum curvature or to the point at which the slope of the curve is equal to 1.The wetted perimeter-discharge curve of a natural river is only part of the complete curve.Thus,the instream flow calculated by the traditional method is the minimum or maximum discharge.The new criterion for defining the breakpoint of the wetted perimeter-discharge curve is that the slope at the breakpoint is a relative maximum,the second-largest slope.The discharges at the breakpoints corresponded to the minimum flow levels required to maintain the ecological function of the river.The minimum instream flow requirements(MIFRs) of four typical reaches,Zhuba,Daofu,Ganzi and Zumuzu hydrological stations on the West Course of the First Stage Project of the South-North Water Transfer Project(WCFSPSNWTP),are calculated using an improved wetted perimeter method(IWPM).The results show that the MIFRs of Zhuba,Daofu,Ganzi and Zumuzu are approximately 9.06-14.5 m 3 s-1,20.7-43.5 m3 s-1,38.8-77.2 m 3 s-1 and 40.4-59.5 m 3 s-1,corresponding to 11.7%-33.9%,14.2%-37.6%,12.4%-28.4% and 17.5%-30.2%,respectively of the annual average flow(AAF).These MIFRs can maintain good ecological function in a river according to the criterion furnished by the Tennant method.
