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The spectrum of path factorization of bipartite multigraphs

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Science china Mathematics 2007年第7期50卷 1045-1054页

作者： Jian WANG~1 Bei-liang DU~(2.) 1 nantong Vocational college,nantong 2.6007,china 2.department of Mathematics,Suzhou University,Suzhou 2.5006,china 1. nantong Vocational college Nantong 226007 China 2. department of Mathematics Suzhou University Suzhou 215006 China

Let λK m,n be a bipartite multigraph with two partite sets having m and n vertices, respectively. A P v-factorization of λK m,n is a set of edge-disjoint P v-factors of λK m,n which partition the set of edges of λK m,n . When v is an even number, Ushio, Wang and the second author of the paper gave a necessary and sufficient condition for the existence of a P v-factorization of λK m,n . When v is an odd number, we have proposed a conjecture. Very recently, we have proved that the conjecture is true when v = 4k ? 1. In this paper we shall show that the conjecture is true when v = 4k + 1, and then the conjecture is true. That is, we will prove that the necessary and sufficient conditions for the existence of a P 4k+1-factorization of λK m,n are (1) 2.m ? (2. + 1)n, (2. 2.n ? (2. + 1)m, (3) m + n ≡ 0 (mod 4k + 1), (4) λ(4k + 1)mn/[4k(m + n)] is an integer.

关键词： bipartite multigraph factorization 05B30 05C70

Relationships between D1 protein, xanthophyll cycle and photodamage-resistant capacity in rice (Orysa sativa L.)

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Chinese Science Bulletin 2000年第17期45卷 1569-1575页

作者： Jl Benhua & JIAO Demao1. Institute of Agrobiological Genetics and Physiology, Jiangsu Academy of Agricultural Sciences, Nanjing 2.0014, china 2. department of Biology , {2. Teachers college, nantong 2.6007, china Correspondence should be addressed to Jiao Demao Institute of Agrobiological Genetics and Physiology Jiangsu Academy of Agricultural Sciences Nanjing China department of Biology Nantong Teachers College Nantong China

Relationships between D1 protein, xanthophyll cycle and subspecific difference of photodamage-resistant capacity have been studied in O. japonica rice varieties 02.2. and 02. (photoinhibition-tolerance) and O. indica rice varieties 3037 and Palghar (photoinhibition-sensitivity) and their reciprocal cross F, hybrids after photoinhibitory treatment. It was shown that PS II photochemical efficiency (Fv /Fm) decreased, and xanthophyll cycle from violaxanthin (V), via anaxanthin (A), to zeaxanthin (Z) was enhanced and non-photochemical quenching (g/v) increased accordingly in SM-pretreated leaves of rice when the synthesis of D1 protein was inhibited, and that there was a decrease in qN and, as a result, more loss of D1 protein and a big decrease in Fv/Fm in DTT-pretreated leaves when xanthophyll cycle was inhibited. O. japonica subspecies had a higher maintaining capacity of D1 protein and a decrease of Fv /Fm in a more narrow range, and exhibited more resistance against photodamage, as compared with O.

关键词： D1 protein non-photochemical quenching photoinhibition of photosynthesis rice xanthophyll cycle.

Mathematic Expression of Kinetic Compensation Effect and Relationship between the Exothermic Decomposition Temperature and Critical Temperature of Thermal Explosion of Eighty-six Energetic Materials

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含能材料 2001年第1期9卷 8-9页

作者： HU Rong zu 1, YANG De suo 2. ZHANG Jiao qiang 3 (1. department of chemistry,Northwest University, Xi′an 710065,{2. 2. department of chemistry and Chemical Engineering, Baoji college of Arts and Science, Baoji 72.007,{2. 3. department of 西北大学陕西西安 710065 宝鸡文理学院陕西 721007 西北工业大学陕西西安 710072

Two relationships are established using the least squares method,between the kinetic parameters (the apparent activation energy and pre exponential constant),and the exothermic decomposition temperature and ther... 详细信息

关键词： critical temperature of thermal explosion decomposition temperature DSC energetic materials.

Theoretical study on thermal decomposition of azoisobutyronitrile in ground state

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Science china chemistry 2004年第5期47卷 373-380页

作者： SUN Chengke1,2. ZHAO Hongmei1 & LI Zonghe1 1. department of chemistry, Beijing Normal University, Beijing 100875,{2. 2. department of chemistry, Qujing Normal college, Qujing 655000,{2. 1. department of chemistry Beijing Normal University 100875 Beijing China 2. department of chemistry Qujing Normal College 655000 Qujing China

The thermal decomposition mechanisms of azoisobutyronitrile (AIBN) in the ground state have been investigated systematically. Based on the potential energy surfaces (PES) of various possible dissociation paths obtained using the semiempirical AM1 method with partial optimization, the density function theory B3LYP/6-311G* method was employed to optimize the geometric parameters of the reactants, the intermediates, the products and the transition states, which were further confirmed by the vibrational analysis. The obtained results show that the re- action process of the two-bond (three-body) simultaneous cleavage Me2.CN)C─ N=N─ C(CN)Me2. 2.e2.CN)C?+N2.is much more favorable than the reaction process of the two one- bond asynchronous cleavage Me2.CN)CN=N─C(CN)Me2.? Me2.CN)CN=N?+ Me2.CN)C?? Me2.CN)C?+ N2. It was suggested that the electron shrinking effect of double bond (─N=N─) in AIBN and the stabilities of the Me2.CN)C?radical as well as N2.molecule are main factors of leading to the reaction proceeding in the former pathway. The calculation results were consistent with all the experimental facts.

关键词： azoisobutyronitrile, radicals, thermal decomposition, density function theory (DFT).

P_(4k-1)-factorization of complete bipartite graphs

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Science china Mathematics 2005年第4期48卷 539-547页

作者： DU Beiliang & WANG Jian department of Mathematics, Suzhou University, Suzhou 2.5006, china {2. Vocational college, nantong 2.6007, china 1. department of Mathematics Suzhou University 215006 Suzhou China 2. nantong Vocational college 226007 Nantong China

Let Km,n be a complete bipartite graph with two partite sets having m and n vertices, respectively. A Pv-factorization of Km,n is a set of edge-disjoint pv-factors of Km,n which partition the set of edges of Km,n. When v is an even number, Wang and Ushio gave a necessary and sufficient condition for the existence of Pv-factorization of Km,*** v is an odd number, Ushio in 1993 proposed a conjecture. However, up to now we only know that Ushio Conjecture is true for v = 3. In this paper we will show that Ushio Conjecture is true when v = 4k - 1. That is, we shall prove that a necessary and sufficient condition for the existence of a P4k-1-factorization of Km,n is (1) (2. - 1)m ≤ 2.n, (2. (2. -1)n≤2.m, (3) m + n ≡ 0 (mod 4k - 1), (4) (4k -1)mn/[2.2. -1)(m + n)] is an integer.

关键词： complete bipartite graph, factorization, Ushio Conjecture.

Fuzzy controllers based on some fuzzy implication operators and their response functions

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Progress in Natural Science:Materials International 2004年第1期14卷 16-21页

作者： LI Hongxing 1*, YOU Fei 1 and PENG Jiayin 2.1. department of Mathematics, Beijing Normal University, Beijing 100875, china 2. department of Mathematics, Neijiang Teacher's college, Neijiang 641112. china) Beijing Normal Univ Dept Math Beijing 100875 Peoples R China

The fuzzy controllers constructed by 2. fuzzy implication operators based on CRI algorithm and their response functions are discussed. The conclusions show that the fuzzy controllers constructed by 9 fuzzy implication operators are universal approximators to continuous functions and can be used in practical fuzzy control systems. And these 9 fuzzy implication operators except for Einstein operator intersection are all the adjoint pairs of some fuzzy implication operators. Besides, there are 3 other fuzzy controllers formed by fuzzy implication operators being regarded approximately as fitted functions.

关键词： fuzzy implication operators CRI algorithm fuzzy controllers response functions universal approximators

Approach to synthesis of novel chiral 3-chloro-2.5H)- furanone and its application in asymmetric reactions

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Chinese Science Bulletin 2000年第8期45卷 711-716页

作者： HUANG Hui & CHEN Qinghua1. department of chemistry, Tonghua Teacher’s {2., Tonghua 134002. china 2. department of chemistry, Beijing Normal University, Beijing 100875, china department of chemistry Tonghua Teacher’s College Tonghua China department of chemistry Beijing Normal University Beijing China

The synthetic method of the novel chiral synthon, 5-/-menthyloxy-3-chloro-2.(5H)-furanone 5a and its application in asymmetric reactions were investigated. 5a is easily obtained in highly optical purity, and acts as a stable acceptor of Michael addition with oxygen nucleophiles in tandem double Michael addition / internal nucieophilic substitution to offer the spiro-cyclopropane derivative containing four stereogenic centers 8, which it is difficult to obtain by routine methods. The synthetic methods for 5a and 8 are reported in detail and the new compounds are identified on the basis of their analytical data and spectroscopic data, such as UV, IR, H NMR,13 C NMR, MS and elementary analysis. The absolute configuration of the interesting spiro-cyclopropanes, spiro [1-chloro-4-(/-menthyloxy)-5-oxo-6-oxa-biscyclo[3.1.0]hexane-2.3i(4’-/-menthyloxy-5’-/-menthyloxy- butyrolactone)] 8 was established by X-ray crystallography. This result can provide important synthetic strategy in synthesis of some complex

关键词： new chiral synthon. 5-l-menthyloxy-3-chloro-2.(5H)-furanone absolute configuration spiro-cyclopropane derivative containing multiple chiral centers.

P_(4k-1)-factorization of bipartite multigraphs

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Science china Mathematics 2006年第7期49卷 961-970页

作者： WANG Jian & DU Beiliang nantong Vocational college,{2., china department of Mathematics, Suzhou University, Suzhou 2.5006, china 1. Vocational college Nantong 226007 China 2. department of Mathematics Suzhou University Suzhou 215006 China

LetλKm,n be a bipartite multigraph with two partite sets having m and n vertices, respectively. A Pν-factorization ofλKm,n is a set of edge-disjoint Pν-factors ofλKm,n which partition the set of edges ofλKm,n. Whenνis an even number, Ushio, Wang and the second author of the paper gave a necessary and sufficient condition for the existence of a Pν-factorization ofλKm,n. When v is an odd number, we proposed a conjecture. However, up to now we only know that the conjecture is true forν= 3. In this paper we will show that the conjecture is true whenν= 4k-1. That is, we shall prove that a necessary and sufficient condition for the existence of a P4k-1-factorization ofλKm,n is (1) (2.-1)m≤2.n, (2. (2.-1)n≤2.m, (3)m + n = 0 (mod 4k-1), (4)λ(4k-1)mn/[2.2.-1)(m + n)] is an integer.

关键词： bipartite multigraph, factor, factorization.

The proof of Ushio's conjecture concerning path factorization of complete bipartite graphs

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Science china Mathematics 2006年第3期49卷 289-299页

作者： DU Beiliang & WANG Jian department of Mathematics, Suzhou University, Suzhou 2.5006, china {2. Vocational college, nantong 2.6007, china department of Mathematics Suzhou University Suzhou 215006 China nantong Vocational college Nantong 226007 China

Let Km,n be a complete bipartite graph with two partite sets having m and n vertices, respectively. A Pv-factorization of Km,n is a set of edge-disjoint Pv-factors of Km,n which partition the set of edges of Km,n. When v is an even number, Wang and Ushio gave a necessary and sufficient condition for existence of Pv-factorization of Km,n. When k is an odd number, Ushio in 1993 proposed a conjecture. Very recently, we have proved that Ushio's conjecture is true when v = 4k - 1. In this paper we shall show that Ushio Conjecture is true when v = 4k + 1, and then Ushio's conjecture is true. That is, we will prove that a necessary and sufficient condition for the existence of a P4k+1-factorization of Km,n is (i) 2.m ≤ (2. + 1)n,(ii) 2.n ≤ (2. + 1)m, (iii) m + n ≡ 0 (mod 4k + 1), (iv) (4k + 1)mn/[4k(m + n)] is an integer.

关键词： complete bipartite graph, factorization, Ushio Conjecture.