By investigating the properties of Hellinger-Toeplitz topologies, we establish a general version of Kalton's cioed graph theorem. From this general version, we deduce a number of new closed graph theorems, which a...By investigating the properties of Hellinger-Toeplitz topologies, we establish a general version of Kalton's cioed graph theorem. From this general version, we deduce a number of new closed graph theorems, which are convenient for application. Particularly we improve some results of Kalton.展开更多
By introducing the notions of L-spaces and L_r-spaces, a complete generalization of Kalton's closed graph theorem is obtained. It points out the class of L_r-spaces is the maximal class of range spaces for the clo...By introducing the notions of L-spaces and L_r-spaces, a complete generalization of Kalton's closed graph theorem is obtained. It points out the class of L_r-spaces is the maximal class of range spaces for the closed graph theorem when the class of domain spaces is the class of Mackey spaces with weakly * sequentially complete dual.Some examples are constructed showing that the class of L_r-spaces is strictly larger than the class of separable B_r-complete spaces.Some properties of L-spaces and L_r-spaces are discussed and the relations between B-complete (resp. B_r-complete) spaces and L-spaces (resp. L_r-spaces) are given.展开更多
A digraph D is supereulerian if D has a spanning eulerian subdigraph. Bang- Jensen and Thomasse conjectured that if the arc-strong connectivity ）,（D） of α digraph D is not less than the independence number α（D）...A digraph D is supereulerian if D has a spanning eulerian subdigraph. Bang- Jensen and Thomasse conjectured that if the arc-strong connectivity ）,（D） of α digraph D is not less than the independence number α（D）, then D is supereulerian. In this paper, we prove that if D is an extended cycle, an extended hamiltonian digraph, an arc-locally semicomplete digraph, an extended arc-locally semicomplete digraph, an extension of two kinds of eulerian digraph, a hypo-semicomplete digraph or an extended hypo-semicomplete digraph satisfying λ（D） ≥α（D）, then D is supereulerian.展开更多
Let CCM denote the class of closed graphs with Cohen-Macaulay binomial edge ideals and PIG denote the class of proper interval graphs.Then CCM⊆PIG The PIG-completion problem is a classical problem in graph theory as w...Let CCM denote the class of closed graphs with Cohen-Macaulay binomial edge ideals and PIG denote the class of proper interval graphs.Then CCM⊆PIG The PIG-completion problem is a classical problem in graph theory as well as in molecular biology,and this problem is known to be NP-hard.In this paper,we study the CCM-completion problem.We give a method to construct all possible CCM-completions of a graph.We find the CCM-completion number and the set of all minimal CCM-completions for a large class of graphs.Moreover,for this class,we give a polynomial-time algorithm to compute the CCM-completion number and a minimum CCM-completion of a given graph.The unmixedness and Cohen-Macaulay properties of binomial edge ideals of induced subgraphs are investigated.Also,we discuss the accessible graph completion and the Cohen-Macaulay property of binomial edge ideals of whisker graphs.展开更多
Herzog,Hibi,Hreinddttir et al.introduced the class of closed graphs,and they proved that the binomial edge ideal JG of a graph G has quadratic GrSbner bases if G is closed.In this paper,we introduce the class of weakl...Herzog,Hibi,Hreinddttir et al.introduced the class of closed graphs,and they proved that the binomial edge ideal JG of a graph G has quadratic GrSbner bases if G is closed.In this paper,we introduce the class of weakly closed graphs as a generalization of the closed graph,and we prove that the quotient ring S/JG of the polynomial ring S=K[x1,...,xn,y1,...,yn]with K a field and n=|V(G)|is F-pure if G is weakly closed.This fact is a generalization of Ohtani's theorem.展开更多
针对大场景激光里程计误差累积及其导致的纯激光闭环检测失效问题,提出了一种融合视觉闭环的激光里程计算法。首先采用点云分割技术实现基于特征的激光里程计算法,然后结合视觉检测的闭环约束进行全局位姿图优化,实现高精度位姿估计及...针对大场景激光里程计误差累积及其导致的纯激光闭环检测失效问题,提出了一种融合视觉闭环的激光里程计算法。首先采用点云分割技术实现基于特征的激光里程计算法,然后结合视觉检测的闭环约束进行全局位姿图优化,实现高精度位姿估计及地图构建。采用KITTI开源数据集进行实验,并将本文算法与LOAM(LiDAR odometry and mapping)算法和LeGO-LOAM(lightweight and ground-optimized-LOAM)算法进行对比。结果表明,本文算法的位姿估计精度最高,综合位姿估计仅需31.3 ms,满足自动驾驶汽车实时定位与建图需求。展开更多
文摘By investigating the properties of Hellinger-Toeplitz topologies, we establish a general version of Kalton's cioed graph theorem. From this general version, we deduce a number of new closed graph theorems, which are convenient for application. Particularly we improve some results of Kalton.
文摘By introducing the notions of L-spaces and L_r-spaces, a complete generalization of Kalton's closed graph theorem is obtained. It points out the class of L_r-spaces is the maximal class of range spaces for the closed graph theorem when the class of domain spaces is the class of Mackey spaces with weakly * sequentially complete dual.Some examples are constructed showing that the class of L_r-spaces is strictly larger than the class of separable B_r-complete spaces.Some properties of L-spaces and L_r-spaces are discussed and the relations between B-complete (resp. B_r-complete) spaces and L-spaces (resp. L_r-spaces) are given.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1176107161363020)+1 种基金Science and Technology Innovation Project of Xinjiang Normal University(Grant No.XSY201602013)the"13th Five-Year"Plan for Key Discipline Mathematics of Xinjiang Normal University(Grant No.17SDKD1107)
文摘A digraph D is supereulerian if D has a spanning eulerian subdigraph. Bang- Jensen and Thomasse conjectured that if the arc-strong connectivity ）,（D） of α digraph D is not less than the independence number α（D）, then D is supereulerian. In this paper, we prove that if D is an extended cycle, an extended hamiltonian digraph, an arc-locally semicomplete digraph, an extended arc-locally semicomplete digraph, an extension of two kinds of eulerian digraph, a hypo-semicomplete digraph or an extended hypo-semicomplete digraph satisfying λ（D） ≥α（D）, then D is supereulerian.
文摘Let CCM denote the class of closed graphs with Cohen-Macaulay binomial edge ideals and PIG denote the class of proper interval graphs.Then CCM⊆PIG The PIG-completion problem is a classical problem in graph theory as well as in molecular biology,and this problem is known to be NP-hard.In this paper,we study the CCM-completion problem.We give a method to construct all possible CCM-completions of a graph.We find the CCM-completion number and the set of all minimal CCM-completions for a large class of graphs.Moreover,for this class,we give a polynomial-time algorithm to compute the CCM-completion number and a minimum CCM-completion of a given graph.The unmixedness and Cohen-Macaulay properties of binomial edge ideals of induced subgraphs are investigated.Also,we discuss the accessible graph completion and the Cohen-Macaulay property of binomial edge ideals of whisker graphs.
文摘Herzog,Hibi,Hreinddttir et al.introduced the class of closed graphs,and they proved that the binomial edge ideal JG of a graph G has quadratic GrSbner bases if G is closed.In this paper,we introduce the class of weakly closed graphs as a generalization of the closed graph,and we prove that the quotient ring S/JG of the polynomial ring S=K[x1,...,xn,y1,...,yn]with K a field and n=|V(G)|is F-pure if G is weakly closed.This fact is a generalization of Ohtani's theorem.
文摘针对大场景激光里程计误差累积及其导致的纯激光闭环检测失效问题,提出了一种融合视觉闭环的激光里程计算法。首先采用点云分割技术实现基于特征的激光里程计算法,然后结合视觉检测的闭环约束进行全局位姿图优化,实现高精度位姿估计及地图构建。采用KITTI开源数据集进行实验,并将本文算法与LOAM(LiDAR odometry and mapping)算法和LeGO-LOAM(lightweight and ground-optimized-LOAM)算法进行对比。结果表明,本文算法的位姿估计精度最高,综合位姿估计仅需31.3 ms,满足自动驾驶汽车实时定位与建图需求。
