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Using the Eigenvalue Partition to Compute the Automorphism Group
HAO Jian-Qiang,GONG Yun-Zhan,LIU Hong-Zhi 보안공학연구지원센터 2016 International Journal of Hybrid Information Techno Vol.9 No.6
To solve the automorphism group of a graph is a fundamental problem in graph theory. Moreover, it usually is an essential process for graph isomorphism testing. At present, because existing algorithms ordinarily cannot efficiently compute the automorphism group of a graph, ones cannot entirely resolve the graph isomorphism problem. To calculate the automorphism group of a weighted graph, first, briefly review the history of automorphism. Second, introduce the concept of eigenvalue partition. Third, using algebraic methods, examine not only the relationships between the diagonal form of an adjacency matrix and its eigenvalues and eigenvectors, but also the relationships between its eigenvalues and eigenvectors and the automorphism group. Furthermore, prove Theorem 2 to 8. In addition, propose Conjecture 1 and three open problems. By these theorems, present a novel method to resolve the automorphism group of a weighted graph. If a graph has no duplicate eigenvalues and Conjecture 1 is true, it can determine the automorphism group of a weighted graph in polynomial time by the method. Although this method has certain limitations and needs improvements, it is theoretically a necessary complement to solve the automorphism group. Finally, it shows the close relationships that exist between an orthogonal matrix and a permutation matrix, also an orthogonal matrix and an automorphism.
Apply Partition Tree to Compute Canonical Labelings of Graphs
HAO Jian-Qiang,GONG Yun-Zhan,Tan Li,Duan Da-Gao 보안공학연구지원센터 2016 International Journal of Grid and Distributed Comp Vol.9 No.5
This paper establishes a theoretical framework by defining a set of concepts useful for classifying graphs and computing the canonical labeling Cmax(G) of a given undirected graph G, which including the partition tree PartT(G), maximum partition tree MaxPT(G), centre subgraph Cen(G), standard regular sequence SRQ(G), standard maximum regular sequence SMRQ(G), and so on. The implementations of algorithms 1 to 5 show how to calculate them accordingly. The worst time complexities of algorithms 1, 2, 4, and 5 are O(n2) respectively. The time complexity of Algorithm 3 is O(n). By Theorem 3, all leaf nodes of PartT(G) and MaxPT(G) are the regular subgraphs. By Theorem 4 and 5, there exists only one Cen(G) in G. Regular Partition Theorem 6 shows that there exists just one corresponding PartT(G), SRQ(G), MaxPT(G), and SMRQ(G). One can use Classification Theorem 7 to category graphs. Theorem 8 and 9 establish the link between the Cen(G) and the calculation of the first node u1 added into MaxQ(G) corresponding to the canonical labeling Cmax(G) of G. Further, it utilizes the Cen(G) to calculate the first node u1 added into MaxQ(G). The proposed methods can be extended to deal with the directed graphs and weighted graphs.
Hao, Jian,Zou, Run-Hao,Liao, Rui-Jin,Yang, Li-Jun,Liao, Qiang,Zhu, Meng-Zhao The Korean Institute of Electrical Engineers 2018 Journal of Electrical Engineering & Technology Vol.13 No.4
Natural ester is a suitable substitute for mineral oil and has been widely used in AC transformer in many countries. In order to further application of natural ester in direct current (DC) equipment, it is needed to investigate its long term insulation property under DC condition. In this paper, a thermal ageing experiment was conducted for both mineral oil-paper and natural ester-paper insulation. The DC breakdown and space charge characteristics of insulation paper impregnated with natural ester and mineral oil was compared. Results show that the resistivity of the paper immersed in natural ester and mineral oil both increase as the ageing goes on. While insulation paper impregnated with natural ester has higher resistivity and DC breakdown voltage than the paper impregnated with mineral oil. The DC breakdown voltage for the oil impregnated insulation paper being DC pre-stressing is higher than that without pre-stressing. The average DC breakdown field strength difference between the test with pre-stressing and without pre-stressing clearly shows that there is an apparent enhancement effect for the homo-charge injection on the DC breakdown.
Good performance of Sc (0001) surface adsorbing CO molecule
Hao Zhi-Qiang,Yang Jian-Long,Li Hui,Yao Jian-Gang 한국물리학회 2022 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.80 No.9
There is a big discrepancy in terms of calculating the surface energy of the HCP Sc (0001) surface for previous theoretical results. Herein, we used a relatively reasonable method to predict the calculated value (1.263 J/m2), which agrees well with the experimental outcome (1.275 J/m2). Based on this, the adsorption behaviors of CO at different sites, i.e., hollow (H1, H2, and H3), bridge (B1), and top sites (T1), were explored theoretically. The results suggest that hollow sites, particularly the H1 site exhibits a good performance in adsorbing CO molecule, and that the adsorption energy reaches nearly 3.5 eV, which corresponds to a significant elongation of the C–O distance (more than 24%). In addition, the CO adsorbed at the H1 site is seen to be located parallelly at the surface. An obvious substantive variation of the CO molecular orbit of H1 adsorption site is observed.
Jian Hao,Run-Hao Zou,Rui-Jin Liao,Li-Jun Yang,Qiang Liao,Meng-Zhao Zhu 대한전기학회 2018 Journal of Electrical Engineering & Technology Vol.13 No.4
Natural ester is a suitable substitute for mineral oil and has been widely used in AC transformer in many countries. In order to further application of natural ester in direct current (DC) equipment, it is needed to investigate its long term insulation property under DC condition. In this paper, a thermal ageing experiment was conducted for both mineral oil-paper and natural ester-paper insulation. The DC breakdown and space charge characteristics of insulation paper impregnated with natural ester and mineral oil was compared. Results show that the resistivity of the paper immersed in natural ester and mineral oil both increase as the ageing goes on. While insulation paper impregnated with natural ester has higher resistivity and DC breakdown voltage than the paper impregnated with mineral oil. The DC breakdown voltage for the oil impregnated insulation paper being DC prestressing is higher than that without pre-stressing. The average DC breakdown field strength difference between the test with pre-stressing and without pre-stressing clearly shows that there is an apparent enhancement effect for the homo-charge injection on the DC breakdown.
??强(Guo-qiang Hao) 전남대학교 글로벌디아스포라연구소 2016 전남대학교 세계한상문화연구단 국제학술회의 Vol.2016 No.1
In the new period, the survival situation of overseas Chinese is facing new challenges.With the field research method in anthropology, from the economic interactions, cross-national marriage, language learning and communication etc are described in detail the Laos FengSha Wan in new overseas Chinese survival strategy, thereby Analytical new overseas Chinese in the process of interaction between Laos shown from spontaneous to the coexistence of the concept of change.
Chiral Pool Synthesis of N-Cbz-cis-(3R,4R)-3-methylamino-4-methylpiperidine from L-Malic acid
Hao, Bao-Yu,Liu, Jin-Qiang,Zhang, Wei-Han,Chen, Xin-Zhi Korean Chemical Society 2013 Bulletin of the Korean Chemical Society Vol.34 No.5
A new synthetic route to N-Cbz-cis-(3R,4R)-3-methylamino-4-methylpiperidine, key intermediate for CP-690,550, was disclosed with L-malic acid as the chiral pool starting material. The title compound was obtained in 16 steps with a total yield of 26% and more than 98% ee.
( Qiang Li ),( Yu Fu ),( Qun Sun ),( Pierre Sourzat ),( Mei Yang ),( Chengyi Liu ),( Hao Tan ),( Lei Ye ),( Jie Zou ),( Chenguang Wu ),( Bo Zhang ),( Xiaolin Li ) 한국균학회 2018 Mycobiology Vol.46 No.1
The aim of this study was to investigate the pattern of distribution of mating type (MAT) genes of Tuber indicum in ectomycorhizosphere soils from natural T. indicum-producing areas and cultivated truffle orchards and ascocarp samples from different regions. Quantitative real-time PCR and multiplex PCR were used to weight the copy numbers of MAT1-1-1 and MAT1-2-1 in natural truffle soils and cultivated orchard soils. The effect of limestone on the pattern of truffle MAT genes and the correlation between soil properties and the proportion of MAT genes were also assessed. These results indicated that an uneven and nonrandom distribution of MAT genes was common in truffle-producing areas, cultivated truffle orchards, and ascocarps gleba. The competition between the two mating type genes and the expansion of unbalanced distribution was found to be closely related to truffle fructification. Limestone treatments failed to alter the proportion of the two mating type genes in the soil. The content of available phosphorus in soil was significantly correlated with the value of MAT1-1-1/MAT1-2-1 in cultivated and natural ectomycorhizosphere soils. The application of real-time quantitative PCR can provide reference for monitoring the dynamic changes of mating type genes in soil. This study investigates the distributional pattern of T. indicum MAT genes in the ectomycorhizosphere soil and ascocarp gleba from different regions, which may provide a foundation for the cultivation of T. indicum.
Hao, Hu-Jun,Yin, Xian-Hong,Lin, Cui-Wu,Wei, Shui-Qiang Korean Chemical Society 2011 Bulletin of the Korean Chemical Society Vol.32 No.9
Two novel binuclear metal-organic coordination complexes $[Cd_2(L)_2(bpy)_2(H_2O)_2]{\cdot}6H_2O$ (1), $[Cd_2(L)_2(phen)_2-(H_2O)_2]{\cdot}2H_2O$ (2) (where L = 2-methylquinoline-3,4-dicarboxylate dianion, bpy = 2,2'-bipyridine, phen = 1,10-phenanthroline) have been synthesized under hydrothermal conditions and characterized by single crystal Xray diffraction, spectral method (IR), elemental analysis and thermal gravimetric analysis (TGA). Both 1 and 2 consist of two Cd(II) atoms bridged by two monoatomic bridging carboxylate groups from two L ligands, and the second carboxylate group of each L is monodentately coordinated to Cd(II), creating a sevenmembered chelating ring. The coordination at each metal nucleus is completed by a water molecule and a chelating bidentate molecule. The 3D structures of the complexes are stabilized by ${\pi}-{\pi}$ stacking interactions and hydrogen-bonds.