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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, nantong 2.6007, china Department of Mathematics, Suzhou University, Suzhou 215006, 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) (2k-1)m≤2kn, (2) (2k-1)n≤2km, (3)m + n = 0 (mod 4k-1), (4)λ(4k-1)mn/[2(2k-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 215006, china nantong 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) 2km ≤ (2k + 1)n,(ii) 2kn ≤ (2k + 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.

K_(p,q)-factorization of complete bipartite graphs

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Science china Mathematics 2004年第3期47卷 473-479页

作者： DU Beiliang WANG Jian Department of Mathematics, Suzhou University, Suzhou 215006, china nantong 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 completebipartite graph with two partite sets having m and n vertices,respectively. A Kp,q-factorization of Km,n is a set ofedge-disjoint Kp,q-factors of Km,n which partition theset of edges of Km,n. When p=1 and q is a prime number,Wang, in his paper 'On K1,k-factorizations of a completebipartite graph' (Discrete Math, 1994, 126: 359-364),investigated the K1,q-factorization of Km,n and gave asufficient condition for such a factorization to exist. In the paper'K1,k-factorizations of complete bipartite graphs' (DiscreteMath, 2002, 259: 301-306), Du and Wang extended Wang's resultto the case that q is any positive integer. In this paper, we give a sufficient condition for Km,n to have aKp,q-factorization. As a special case, it is shown that theMartin's BAC conjecture is true when p:q=k:(k+1) for any positiveinteger k.

关键词： complete bipartite graph factorization HUBMFS 2 scheme

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 215006,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) 2km ? (2k + 1)n, (2) 2kn ? (2k + 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

AREA FUNCTIONS ON HARDY SPACES ASSOCIATED TO SCHRDINGER OPERATORS

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Acta Mathematica Scientia 2003年第4期23卷 521-530页

作者：朱月萍 Department of Mathematics Nantong Teachers' College Nantong 226007 China

In this paper, the author gives a characterization of atomic Hardy spaces associated to Schrodinger operators by using area functions, and hence gets the dual spaces of atomic Hardy spaces.

关键词： Square function area function Hardy spaces Schrodinger operators

On the general expressions of finite Hankel transform

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Science china(Physics,Mechanics & Astronomy) 2010年第11期53卷 2125-2130页

作者： JIANG Quan 1,2 & GAO CunFa 1 1 college of Aerospace Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,china 2 School of Civil Engineering,nantong University,nantong 226019,china 1. college of Aerospace Engineering Nanjing University of Aeronautics and Astronautics Nanjing 210016 China2. School of Civil Engineering Nantong University Nantong 226019 China

The general expressions of finite Hankel transform are naturally deduced with the help of the property of Bessel *** equations in this paper can degenerate into three kinds of boundaries since all the coefficients in the boundary conditions are taken into *** results can be adopted in solving physics problems involving the finite Hankel transform.

关键词： hankel transform bessel function finite integral

Potential control of horseradish peroxidase immobilization on gold electrode

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中国科学：化学英文版 2004年第2期47卷 134-141页

作者： GE Cunwang1,2, YU Wei1, LI Changan1, WANG Nanping2 & GU Ning1 1. Key Laboratory of Molecular and Biomolecular Electronics (Southeast University), Ministry of Education, Research Center for Nano-scale Science and Technology, Southeast University, Nanjing 210096, china 2. Department of Chemistry, nantong Teachers college, nantong 2.6007, china 1. Key Laboratory of Molecular and Biomolecular Electronics (Southeast University) Ministry of Education Research Center for Nano-scale Science and Technology Southeast University 210096 Nanjing China 2. Department of Chemistry Nantong Teachers College 226007 Nantong China

A new approach based on potential control was firstly used for the immobilization of horseradish peroxidase (HRP) as the model protein. The self-assembly monolayer (SAM) was prepared with 2-aminoethanethiol (AET) on the gold electrode. The charge on HRP was adjusted by means of the acidity of the phosphate buffer solution (PBS) for dissolving the HRP. The in-fluence of electric potential on HRP immobilization was investigated by means of colorimetric immunoassay of enzyme-substrate interaction (CIESI) using an automatic plate reader. The HRP modified electrodes were characterized with X-ray photoelectron spectroscopy (XPS) as well as atomic force microscope (AFM) on template-stripped gold surface. The potential for maximum immobilization of HRP was near the zero charge potential. The result indicates that controlled potential can affect the course of HRP immobilization without the loss of enzymic activity. It is of great significance for the control of biomolecular self-assembly and the intrinsic electric device.

关键词： electric potential control, horseradish peroxidase, immobilization, gold electrode, self-assembly.

Comparison of Hypolipidemic Effect of Refined Konjac Meal With Several Common Dietary Fibers and Their Mechanisms of Action

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Biomedical and Environmental Sciences 1997年第1期10卷 27-37页

作者： WU JIE AND PENG SHU-SHENG (Department of Nutrition and Food Hygiene, nantong Medical college, nantong City, 226001, Jiangsu, china Department of Nutrition and Food Hygiene, West china University of Medical Sciences,Chengdu, Sichuan, china) Department of Nutrition and Food Hygiene Nantong Medical College Jiangsu China.

The effects of RKM in comparison with pectin, algin and agar on lipid levels in serum and liver and on liver histopathology in rats were studied. In addition, the effects of all the tested materials on the composition and output of fecal bile acid were observed. All four kinds of dietary fiber were given at a level of 5% of diet to young male rats of Wistar strain fed on a lipid-rich diet contalning 5 % lard, 1% cholesteral and 0. 25 % cholate. All the dietary fibers tested have similar effects on serum lipid composition. In all groups, these substances prevent ed increases in total cholesterol in fasting serum, but the level of triglyceride was *** concentrations of totaI cholesterol and triglyceride in the liver were lower in the RKM group than in the control group and the other three groups. Hepatic histopathological exami nation also showed the most significant lipotropic effect in the RKM group. The daily output of fecal bile acids (CDCA+GDCA) was significantly increased in the four experimental groups than in the normal group and the control group. The increase of CDCA was more significant than GDCA, suggesting that the increase of fecal bile acids, especially CDCA, may be one of the mechanisms by which RKM and the other three dietary fibers exerts a hypocholesterolemic effect

关键词： acid Am Br Comparison of Hypolipidemic Effect of Refined Konjac Meal With Several Common Dietary Fibers and Their Mechanisms of Action CDCA

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 210014, china 2. Department of Biology , nantong 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 02428 and 029 (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.