We first investigate the translative containment measure for convex domain K0 to contain, or to be contained in, the homothetic copy of another convex domain K1, i.e., given two convex domains K0, K1 of areas A0, A1, ...We first investigate the translative containment measure for convex domain K0 to contain, or to be contained in, the homothetic copy of another convex domain K1, i.e., given two convex domains K0, K1 of areas A0, A1, respectively, in the Euclidean plane R2, is there a translation T so that t(T K1) K0 or t(T K1) ? K0 for t > 0? Via the translative kinematic formulas of Poincar′e and Blaschke in integral geometry,we estimate the symmetric mixed isohomothetic deficit σ2(K0, K1) ≡ A201- A0A1, where A01 is the mixed area of K0 and K1. We obtain a sufficient condition for K0 to contain, or to be contained in, t(T K1). We obtain some Bonnesen-style symmetric mixed isohomothetic inequalities and reverse Bonnesen-style symmetric mixed isohomothetic inequalities. These symmetric mixed isohomothetic inequalities obtained are known as Bonnesen-style isopermetric inequalities and reverse Bonnesen-style isopermetric inequalities if one of domains is a disc. As direct consequences, we obtain some inequalities that strengthen the known Minkowski inequality for mixed areas and the Bonnesen-Blaschke-Flanders inequality.展开更多
This work focuses on the potential impacts of the autonomous vehicles in a mixed traffic condition represented in traffic simulator Simulation of Urban MObility(SUMO)with real traffic flow.Specifically,real traffic fl...This work focuses on the potential impacts of the autonomous vehicles in a mixed traffic condition represented in traffic simulator Simulation of Urban MObility(SUMO)with real traffic flow.Specifically,real traffic flow and speed data collected in 2002 and 2019 in Gothenburg were used to simulate daily flow variation in SUMO.In order to predict the most likely drawbacks during the transition from a traffic consisting only manually driven vehicles to a traffic consisting only fully-autonomous vehicles,this study focuses on mixed traffic with different percentages of autonomous and manually driven vehicles.To realize this aim,several parameters of the car following and lane change models of autonomous vehicles are investigated in this paper.Along with the fundamental diagram,the number of lane changes and the number of conflicts are analyzed and studied as measures for improving road safety and efficiency.The study highlights that the autonomous vehicles’features that improve safety and efficiency in 100%autonomous and mixed traffic are different,and the ability of autonomous vehicles to switch between mixed and autonomous driving styles,and vice versa depending on the scenario,is necessary.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.1127130211161007 and 11401486)+1 种基金the Ph.D.Program of Higher Education Research Fund(Grant No.2012182110020)Guizhou Foundation for Science and Technology(Grant No.LKS[2011]6)
文摘We first investigate the translative containment measure for convex domain K0 to contain, or to be contained in, the homothetic copy of another convex domain K1, i.e., given two convex domains K0, K1 of areas A0, A1, respectively, in the Euclidean plane R2, is there a translation T so that t(T K1) K0 or t(T K1) ? K0 for t > 0? Via the translative kinematic formulas of Poincar′e and Blaschke in integral geometry,we estimate the symmetric mixed isohomothetic deficit σ2(K0, K1) ≡ A201- A0A1, where A01 is the mixed area of K0 and K1. We obtain a sufficient condition for K0 to contain, or to be contained in, t(T K1). We obtain some Bonnesen-style symmetric mixed isohomothetic inequalities and reverse Bonnesen-style symmetric mixed isohomothetic inequalities. These symmetric mixed isohomothetic inequalities obtained are known as Bonnesen-style isopermetric inequalities and reverse Bonnesen-style isopermetric inequalities if one of domains is a disc. As direct consequences, we obtain some inequalities that strengthen the known Minkowski inequality for mixed areas and the Bonnesen-Blaschke-Flanders inequality.
文摘This work focuses on the potential impacts of the autonomous vehicles in a mixed traffic condition represented in traffic simulator Simulation of Urban MObility(SUMO)with real traffic flow.Specifically,real traffic flow and speed data collected in 2002 and 2019 in Gothenburg were used to simulate daily flow variation in SUMO.In order to predict the most likely drawbacks during the transition from a traffic consisting only manually driven vehicles to a traffic consisting only fully-autonomous vehicles,this study focuses on mixed traffic with different percentages of autonomous and manually driven vehicles.To realize this aim,several parameters of the car following and lane change models of autonomous vehicles are investigated in this paper.Along with the fundamental diagram,the number of lane changes and the number of conflicts are analyzed and studied as measures for improving road safety and efficiency.The study highlights that the autonomous vehicles’features that improve safety and efficiency in 100%autonomous and mixed traffic are different,and the ability of autonomous vehicles to switch between mixed and autonomous driving styles,and vice versa depending on the scenario,is necessary.
