We give heat kernel estimates on Julia sets J（f;） for quadratic polynomials f c（z） = z;+ c for c in the main cardioid or the ±1/k-bulbs where k ≥ 2. First we use external ray parametrization to construct a r...We give heat kernel estimates on Julia sets J（f;） for quadratic polynomials f c（z） = z;+ c for c in the main cardioid or the ±1/k-bulbs where k ≥ 2. First we use external ray parametrization to construct a regular, strongly local and conservative Dirichlet form on Julia set. Then we show that this Dirichlet form is a resistance form and the corresponding resistance metric induces the same topology as Euclidean metric. Finally, we give heat kernel estimates under the resistance metric.展开更多
In order to quantitatively analyze air traffic operation complexity,multidimensional metrics were selected based on the operational characteristics of traffic flow.The kernel principal component analysis method was ut...In order to quantitatively analyze air traffic operation complexity,multidimensional metrics were selected based on the operational characteristics of traffic flow.The kernel principal component analysis method was utilized to reduce the dimensionality of metrics,therefore to extract crucial information in the metrics.The hierarchical clustering method was used to analyze the complexity of different airspace.Fourteen sectors of Guangzhou Area Control Center were taken as samples.The operation complexity of traffic situation in each sector was calculated based on real flight radar data.Clustering analysis verified the feasibility and rationality of the method,and provided a reference for airspace operation and management.展开更多
文摘We give heat kernel estimates on Julia sets J（f;） for quadratic polynomials f c（z） = z;+ c for c in the main cardioid or the ±1/k-bulbs where k ≥ 2. First we use external ray parametrization to construct a regular, strongly local and conservative Dirichlet form on Julia set. Then we show that this Dirichlet form is a resistance form and the corresponding resistance metric induces the same topology as Euclidean metric. Finally, we give heat kernel estimates under the resistance metric.
基金co-supported by the National Natural Science Foundation of China(No.61304190)the Fundamental Research Funds for the Central Universities of China(No.NJ20150030)the Youth Science and Technology Innovation Fund(No.NS2014067)
文摘In order to quantitatively analyze air traffic operation complexity,multidimensional metrics were selected based on the operational characteristics of traffic flow.The kernel principal component analysis method was utilized to reduce the dimensionality of metrics,therefore to extract crucial information in the metrics.The hierarchical clustering method was used to analyze the complexity of different airspace.Fourteen sectors of Guangzhou Area Control Center were taken as samples.The operation complexity of traffic situation in each sector was calculated based on real flight radar data.Clustering analysis verified the feasibility and rationality of the method,and provided a reference for airspace operation and management.
