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Short cycle structures for graphs on surfaces and an open problem of Mohar and Thomassen

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science china {2. 2006年第2期49卷 212-224页

作者： REN Han & DENG Mo Department of mathematics, East china Normal {2., Shanghai 2.0062. china college of mathematics & information science, northwest Normal {2., lanzhou 730070, china Department of mathematics East China Normal University Shanghai China college of mathematics & information science Northwest Normal University Lanzhou China

In this paper we investigate cycle base structures of a (weighted) graph and show that much information of short cycles is contained in an MCB (i.e., minimum cycle base). After setting up a Hall type theorem for base-transformation, we give a sufficient and necessary condition for a cycle base to be an MCB. Furthermore, we show that the structure of MCB in a (weighted)graph is unique. The property is also true for those having a longest length (although much work has been down in evaluating MCB, little is known for those having a longest length). We use those methods to find out some unknown properties for short cycles sharing particular properties in (unweighted) graphs. As applications, we determine the structures of short cycles in an embedded graph and show that there exist polynomially bounded algorithms in finding a shortest contractible cycle and a shortest two-sided cycle provided such cycles exist. Those answer an open problem of B. Mohar and C. Thomassen.

关键词： cycle base facial cycle graph embedding.

On adjacent-vertex-distinguishing total coloring of graphs

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science china {2. 2005年第3期48卷 289-299页

作者： ZHANG Zhongfu, CHEN Xiang’en, LI Jingwen, YAO Bing, LU Xinzhong & WANG Jianfang college of mathematics and {2. science, northwest Normal university, lanzhou 730070, china Department of Computer, lanzhou Normal college, lanzhou 730070, china Institute of Applied mathematics, lanzhou Jiaotong university, lanzhou 730070, china college of {2. and Electrical Engineering, lanzhou Jiaotong university, lanzhou 730070, china Institute of Applied mathematics, Chinese Academy of sciences, Beijing 100080, china college of mathematics and {2. science Northwest Normal University Lanzhou China Department of Computer Lanzhou Normal College Lanzhou China Institute of Applied mathematics Lanzhou Jiaotong University Lanzhou China college of information and Electrical Engineering Lanzhou Jiaotong University Lanzhou China Institute of Applied mathematics Chinese Academy of Sciences Beijing China

In this paper, we present a new concept of the adjacent-vertex-distinguishing total coloring of graphs (briefly, AVDTC of graphs) and, meanwhile, have obtained the adjacent-vertex-distinguishing total chromatic number... 详细信息

关键词： graph, proper total coloring, adjacent-vertex-distinguishing total coloring, adjacent-vertex-distinguishing total chromatic number.

Near generalized balanced tournament designs with block sizes 4 and 5

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science china {2. 2009年第9期52卷 1927-1938页

作者： SHAN XiuLing1, 2.1 Department of mathematics, Beijing Jiaotong university, Beijing 100044,{2. 2.college of mathematics and information science, Hebei Normal university, Shijiazhuang 050016,{2. Department of mathematics Beijing Jiaotong University Beijing China college of mathematics and {2. science Hebei Normal University Shijiazhuang China

A near generalized balanced tournament design, or an NGBTD(k,m) in short, is a (km+1,k,k-1)-BIBD defined on a (km+1)-set V . Its blocks can be arranged into an m×(km+1) array in such a way that (1) the blocks in every column of the array form a partial parallel class partitioning V\{x} for some point x, and (2. every element of V is contained in precise k cells of each row. In this paper, we completely solve the existence of NGBTD(4,m) and almost completely solve the existence of NGBTD(5,m) with four exceptions.

关键词： near generalized balanced tournament designs frame generalized doubly resolvable packing constructions existence 05B05

L_p-mixed intersection bodies

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science china {2. 2008年第12期51卷 2172-2188页

作者： ZHAO ChangJian Department of information and mathematics {2.s, college of {2., china Jiliang university, Hangzhou 310018, china Department of information and mathematics {2.s College of Science China Jiliang University Hangzhou China

In this paper the author first introduce a new concept of Lp-dual mixed volumes of star bodies which extends the classical dual mixed volumes. Moreover, we extend the notions of Lp- intersection body to Lp-mixed intersection body. Inequalities for Lp-dual mixed volumes of Lp-mixed intersection bodies are established and the results established here provide new estimates for these type of inequalities.

关键词： L p -dual mixed volumes L p -intersection bodies L p -mixed intersection bodies 52.40

Theoretical study of the mechanism for C-H bond activation in spin-forbidden reaction between Ti^+ and C_2._4

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science china Chemistry 2009年第3期52卷 295-303页

作者： LV LingLing1, LIU XinWen1, YUAN Kun1, WANG XiaoFang1 & WANG YongCheng2.1 college of Life science and Chemistry, Tianshui Normal {2., Tianshui 741001, china 2.college of Chemistry and Chemical Engineering, northwest Normal {2., lanzhou 730070, china college of Life science and Chemistry Tianshui Normal University Tianshui China college of Chemistry and Chemical Engineering Northwest Normal University Lanzhou China

The mechanism of the spin-forbidden reaction Ti+(4F, 3d2.s1) + C2.4 → TiC2.2. (2.2. + H2.on both doublet and quartet potential energy surfaces has been investigated at the B3LYP level of theory. Crossing points between the potential energy surfaces and the possible spin inversion process are discussed by means of spin-orbit coupling (SOC) calculations. The strength of the SOC between the low-lying quartet state and the doublet state is 59.3 cm-1 in the intermediate complex IM1-4B2. Thus, the changes of its spin multiplicity may occur from the quartet to the doublet surface to form IM1- 2.1, leading to a sig-nificant decrease in the barrier height on the quartet PES. After the insertion intermediate IM2. two dis-tinct reaction paths on the doublet PES have been found, i.e., a stepwise path and a concerted path. The latter is found to be the lowest energy path on the doublet PES to exothermic TiC2.2. (2.2. + H2.products, with the active barrier of 4.52.kcal/mol. In other words, this reaction proceeds in the following way: Ti++C2.4 →4IC→IM1-4B2.4,2.SC→IM1- 2.1→[2.Sins]→IM2.[2.SMCTS]→IM5→TiC2.2.(2.2.+H2.

关键词： Ti+(4F) and C2.4 spin-forbidden reaction mechanism spin-orbit coupling (SOC) concerted path

Quantum secret sharing between multiparty and multiparty with four states

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science china(Physics,Mechanics & Astronomy) 2007年第5期50卷 572-580页

作者： YAN FengLi1, GAO Ting2.& LI YouCheng1 1 college of Physics and information Engineering, Hebei Normal {2., Shijiazhuang 050016, china 2.college of mathematics and information science, Hebei Normal {2., Shijiazhuang 050016, china college of Physics and information Engineering Hebei Normal University Shijiazhuang China college of mathematics and {2. science Hebei Normal University Shijiazhuang China

A protocol of quantum secret sharing between multiparty and multiparty with four states was presented. It was shown that this protocol can nullify the Trojan horse attack with a multi-photon signal, the fake-signal attack with Einstein-Podolsky- Rosen pairs, the attack with single photons, and the attack with invisible photons. In addition, the upper bounds of the average success probabilities were given for dishonest agent eavesdropping encryption using the fake-signal attack with any two-particle entangled states.

关键词： quantum secret sharing, security, Einstein-Podolsky-Rosen pairs

Robustness and breakup of the spiral wave in a two-dimensional lattice network of neurons

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science china(Physics,Mechanics & Astronomy) 2010年第4期53卷 672-679页

作者： MA Jun 1,2. TANG Jun 2., ZHANG AiHua 3 & JIA Ya 2.1 Department of Physics, lanzhou university of Technology, lanzhou 730050, china 2.Department of Physics, Central china Normal university, Wuhan 430079, china 3 college of Electrical and information Engineering, lanzhou university of Technology, lanzhou 730050, china Department of Physics Lanzhou University of Technology Lanzhou China Department of Physics Central China Normal University Wuhan China college of Electrical and information Engineering Lanzhou University of Technology Lanzhou China

The robustness and breakup of spiral wave in a two-dimensional lattice networks of neurons are investigated. The effect of small- world type connection is often simplified with local regular connection and the long-range connection with certain probability. The network effect on the development of spiral wave can be better described by local regular connection and changeable long-range connection probability than fixed long-range connection probability because the long-range probability could be changeable in realistic biological system. The effect from the changeable probability for long-range connection is simplified by multiplicative noise. At first, a stable rotating spiral wave is developed by using appropriate initial values, parameters and no-flux boundary conditions, and then the effect of networks is investigated. Extensive numerical studies show that spiral wave keeps its alive and robust when the intensity of multiplicative noise is below a certain threshold, otherwise, the breakup of spiral wave occurs. A statistical factor of synchronization in two-dimensional array is defined to study the phase transition of spiral wave by checking the membrane potentials of all neurons corresponding to the critical parameters(the intensity of noise or forcing current)in the curve for factor of synchronization. The Hindmarsh-Rose model is investigated, the Hodgkin-Huxley neuron model in the presence of the channel noise is also studied to check the model independence of our conclusions. And it is found that breakup of spiral wave is easier to be induced by the multiplicative noise in presence of channel noise.

关键词： spiral wave factor of synchronization breakup multiplicative noise robustness

THE LIMITING CASE OF THIELE'S INTERPOLATING CONTINUED FRACTION EXPANSION

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Journal of Computational mathematics 2001年第4期19卷 433-444页

作者： Jie-qing Tan (Institute of Applied mathematics, college of {2. and CAD/CG Division college of Computer & information Hefei, university of Technology, Hefei 2.0009, china) 中国科学技术大学安徽合肥 230009

By means of the determinantal formulae for inverse and reciprocal differences with coincident data points, the limiting case of Thiele's interpolating continued fraction expansion is studied in this paper and given numerical example shows that the limiting Thiele's continued fraction expansion can be determined once for all instead of carrying out computations for each step to obtain each convergent as done in [3].

关键词： Continued fraction Inverse difference Reciprocal difference Expansion.

A characterization for a graphic sequence to be potentially C_r-graphic

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science china {2. 2010年第11期53卷 2893-2905页

作者： YIN JianHua Department of mathematics, college of {2. science and Technology, Hainan university, Haikou 5702.8, china Department of mathematics College of Information Science and Technology Hainan University Haikou China

Let r 3, n r and π = (d1, d2. . . . , dn) be a graphic sequence. If there exists a simple graph G on n vertices having degree sequence π such that G contains Cr (a cycle of length r) as a subgraph, then π is said to be potentially Cr-graphic. Li and Yin (2.04) posed the following problem: characterize π = (d1, d2. . . . , dn) such that π is potentially Cr-graphic for r 3 and n r. Rao and Rao (1972. and Kundu (1973) answered this problem for the case of n = r. In this paper, this problem is solved completely.

关键词： graph cycle degree sequence