This paper considered the Noether normalization of a finitely generated algebra over an algebraically closed field. It gives a necessary and sufficient condition as well as an algorithm for the identification of those...This paper considered the Noether normalization of a finitely generated algebra over an algebraically closed field. It gives a necessary and sufficient condition as well as an algorithm for the identification of those algebraically independent variables, then uses these elements to construct the Noether normalization of this algebra.展开更多
To study the dynamics of mixed traffic flow consisting of motorized and non-motorized vehicles, a carfollowing model based on the principle of collision free and cautious driving is proposed. Lateral friction and over...To study the dynamics of mixed traffic flow consisting of motorized and non-motorized vehicles, a carfollowing model based on the principle of collision free and cautious driving is proposed. Lateral friction and overlapping driving are introduced to describe the interactions between motorized vehicles and non-motorized vehicles. By numerical simulations, the flux-density relation, the temporal-spatial dynamics, and the velocity evolution are investigated in detail The results indicate non-motorized vehicles have a significant impact on the motorized vehicle flow and cause the maximum flux to decline by about 13%. Non-motorized vehicles can decrease the motorized vehicle velocity and cause velocity oscillation when the motorized vehicle density is low. Moreover, non-motorized vehicles show a significant damping effect on the oscillating velocity when the density is medium and high, and such an effect weakens as motorized vehicle density increases. The results also stress the necessity for separating motorized vehicles from non-motorized vehicles.展开更多
文摘This paper considered the Noether normalization of a finitely generated algebra over an algebraically closed field. It gives a necessary and sufficient condition as well as an algorithm for the identification of those algebraically independent variables, then uses these elements to construct the Noether normalization of this algebra.
基金Supported by the National Basic Research Program of China under Grant No.2006CB705500the National Natural Science Foundation of China under Grant Nos.70631001 and 70701004
文摘To study the dynamics of mixed traffic flow consisting of motorized and non-motorized vehicles, a carfollowing model based on the principle of collision free and cautious driving is proposed. Lateral friction and overlapping driving are introduced to describe the interactions between motorized vehicles and non-motorized vehicles. By numerical simulations, the flux-density relation, the temporal-spatial dynamics, and the velocity evolution are investigated in detail The results indicate non-motorized vehicles have a significant impact on the motorized vehicle flow and cause the maximum flux to decline by about 13%. Non-motorized vehicles can decrease the motorized vehicle velocity and cause velocity oscillation when the motorized vehicle density is low. Moreover, non-motorized vehicles show a significant damping effect on the oscillating velocity when the density is medium and high, and such an effect weakens as motorized vehicle density increases. The results also stress the necessity for separating motorized vehicles from non-motorized vehicles.
