In the present paper, a generalization of Steinhaus' chessboard problem of 8 × 8 and that of m×n are given and its solution is proved. Then, Steinhaus' chessboard problem is directly solved as a coro...In the present paper, a generalization of Steinhaus' chessboard problem of 8 × 8 and that of m×n are given and its solution is proved. Then, Steinhaus' chessboard problem is directly solved as a corollary, and the m>n case is solved immediately.展开更多
The edge-tenacity of a graph G(V,E) is denned as min{(|S|+T(G-S))/ω(G-S):S(?)E(G)},where T(G ?S) and ω(G-S), respectively, denote the order of the largest component and the number of the components of G-S. This is a...The edge-tenacity of a graph G(V,E) is denned as min{(|S|+T(G-S))/ω(G-S):S(?)E(G)},where T(G ?S) and ω(G-S), respectively, denote the order of the largest component and the number of the components of G-S. This is a better parameter to measure the stability of a network G, as it takes into account both the quantity and the order of components of the graph G-S. In a previous work, we established a necessary and sufficient condition for a graph to be edge-tenacious. These results are applied to prove that K-trees are strictly edge-tenacious. A number of results are given on the relation of edge-tenacity and other parameters, such as the higher-order edge toughness and the edge-toughness.展开更多
Because the traditional method is difficult to obtain the internal relationshipand association rules of data when dealingwith massive data, a fuzzy clusteringmethod is proposed to analyze massive data. Firstly, the sa...Because the traditional method is difficult to obtain the internal relationshipand association rules of data when dealingwith massive data, a fuzzy clusteringmethod is proposed to analyze massive data. Firstly, the sample matrix wasnormalized through the normalization of sample data. Secondly, a fuzzy equivalencematrix was constructed by using fuzzy clustering method based on thenormalization matrix, and then the fuzzy equivalence matrix was applied as thebasis for dynamic clustering. Finally, a series of classifications were carried out onthe mass data at the cut-set level successively and a dynamic cluster diagram wasgenerated. The experimental results show that using data fuzzy clustering methodcan effectively identify association rules of data sets by multiple iterations ofmassive data, and the clustering process has short running time and good robustness.Therefore, it can be widely applied to the identification and classification ofassociation rules of massive data such as sound, image and natural resources.展开更多
基金The NNSF (10271017, 60373030, 10271048), the Beijing Natural Science Foundation (1012003) the Foundation of Beijing Jiaotong University.
文摘In the present paper, a generalization of Steinhaus' chessboard problem of 8 × 8 and that of m×n are given and its solution is proved. Then, Steinhaus' chessboard problem is directly solved as a corollary, and the m>n case is solved immediately.
基金SuppoSed by the Ministry of Communication(200332922505) the Doctoral Foundation of Ministry of Education(20030151005)
文摘The edge-tenacity of a graph G(V,E) is denned as min{(|S|+T(G-S))/ω(G-S):S(?)E(G)},where T(G ?S) and ω(G-S), respectively, denote the order of the largest component and the number of the components of G-S. This is a better parameter to measure the stability of a network G, as it takes into account both the quantity and the order of components of the graph G-S. In a previous work, we established a necessary and sufficient condition for a graph to be edge-tenacious. These results are applied to prove that K-trees are strictly edge-tenacious. A number of results are given on the relation of edge-tenacity and other parameters, such as the higher-order edge toughness and the edge-toughness.
文摘Because the traditional method is difficult to obtain the internal relationshipand association rules of data when dealingwith massive data, a fuzzy clusteringmethod is proposed to analyze massive data. Firstly, the sample matrix wasnormalized through the normalization of sample data. Secondly, a fuzzy equivalencematrix was constructed by using fuzzy clustering method based on thenormalization matrix, and then the fuzzy equivalence matrix was applied as thebasis for dynamic clustering. Finally, a series of classifications were carried out onthe mass data at the cut-set level successively and a dynamic cluster diagram wasgenerated. The experimental results show that using data fuzzy clustering methodcan effectively identify association rules of data sets by multiple iterations ofmassive data, and the clustering process has short running time and good robustness.Therefore, it can be widely applied to the identification and classification ofassociation rules of massive data such as sound, image and natural resources.
