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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 215006, china Nantong vocational college, Nantong 226007, 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) (2k - 1)m ≤ 2kn, (2) (2k -1)n≤2km, (3) m + n ≡ 0 (mod 4k - 1), (4) (4k -1)mn/[2(2k -1)(m + n)] is an integer.

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

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 226007, 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 226007, 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.

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 226007,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

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 226007, 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

Characteristic analysis for a polynomial-like iterative equation

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Chinese Science Bulletin 1998年第3期43卷 192-196页

作者： Janusz Matkowski 1 and ZHANG Weinian 2 1. department of mathematics, technical University, 43_300 Bielsko_Biala, Poland 2. department of mathematics, Sichuan Union University, Chengdu 610064, china department of mathematics Technical University Bielsko-Biala Poland department of mathematics Sichuan Union University Chengdu China

In the light of Euler’s idea for differential equations,a polynomial_like n _order iterative equation is discussed through analyzing its characteristic polynomial. An unproved result is verified rigorously for the fi... 详细信息

关键词： iterative dynamics functional equation characteristic.

高校二级单位及异地研究院财会监督问题及对策研究

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管理工程师 2024年第5期29卷 27-31页

作者：刘馨阳北京航空航天大学计划财务部北京100022

近年来,财会监督作为党和国家监督体系的重要组成部分,为新时代高校推进财会监督工作提供了根本遵循。基于监督工作的目标和要求,对二级单位及异地研究院财会监督存在的顶层指导和政策宣贯不足、财会人员交流和技术手段不足、合力作用... 详细信息

近年来,财会监督作为党和国家监督体系的重要组成部分,为新时代高校推进财会监督工作提供了根本遵循。基于监督工作的目标和要求,对二级单位及异地研究院财会监督存在的顶层指导和政策宣贯不足、财会人员交流和技术手段不足、合力作用和监督结果应用不足等问题进行深入分析,提出了夯实内控基础、强化制度引领与指导,促进交流学习、提升监督信息化水平,加强统筹管理、发挥财会监督协同合力等具体措施,为推进构建财会监督体系提供建议。

关键词：高校二级单位异地研究院财务监督

Multiary turbo code fitting for unitary space-time modulation and its MAP decoding algorithm

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Science china(Information Sciences) 2010年第12期53卷 2610-2619页

作者： ZHANG DaPeng 1,2,3,LU Ju 1,XU HongJi 1 & ZHANG XingYu 1 1 School of Information Science and Engineering,Shandong University,Jinan 250100,china 2 State Key Laboratory of Integrated Services Networks,Xidian University,Xi'an 710077,china 3 department of Avionics Engineering,First Aeronautical college of the Air Force,xinyang 464000,china 1. School of Information Science and Engineering Shandong University Jinan 250100 China2. State Key Laboratory of Integrated Services Networks Xidian University Xi’an 710077 China3. Department of Avionics Engineering First Aeronautical College of the Air Force Xinyang 464000 China

Unitary space-time modulation(USTM) fits for rapid Rayleigh flat fading channels as it can realize wireless communication when neither the transmitter nor the receiver knows the channel state information(CSI).However,an intrinsic problem is that only when the signal-to-noise ratio(SNR) is high can it give an ideal bit error rate(BER) *** existing bit-wise processing scheme of the combination of turbo code and USTM improves the BER performance and results in an unacceptable calculation complexity,storage and time delay *** this paper,we propose a multiary processing scheme and its corresponding multiary MAP decoding *** results verify that our scheme can reduce the system complexity while keep a good BER ***,we present the first analysis of the reason for the BER performance deterioration of the combination scheme at low SNR with the help of the definition of USTM.

关键词： multiple-input multiple-output unitary space-time modulation turbo code MAP decoding diversity

Characteristics of Hot Ductility in Steels Containing Nb,Ti

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Journal of Iron and Steel Research International 2011年第S1期18卷 372-376页

作者： SONG Hai-wu 1,QI Chang-fa 1,AI Xing-hui 2 (1.Technology Center of Tangshan Iron and Steel Group Company Ltd,Tangshan 063016,Hebei,china 2.department of Metallurgy,Tangshan vocational college of Science and Technology,Tangshan 063001,Hebei,china) Tangshan Iron & Steel Grp Co Ltd Ctr Technol Tangshan 063016 Hebei Peoples R China Tangshan Vocat Coll Sci & Technol Dept Met Tangshan 063001 Hebei Peoples R China

The hot ductility was measured for a series of steels containing Nb and/or Ti with Gleeble-3500 thermo-mechanical *** is found that the effect of austenitizing temperature on hot ductility of Nb-containing steel is *** the austenitizing temperature rises up,the shape of embrittling curve (SEC) from V-shape gradually changes to U-shape,and the range of embrittling temperature widens out and the embrittling degree *** SEC of Nb-containing steel is U-shaped and the embrittling temperature range is about 600-1050℃.The initial temperature of embrittlement on the right is nearly independent of carbon *** SEC of Ti-containing steel is N-shaped and two lowest points are at about 600℃ and the A-F transformation *** SEC of Nb-Ti-containing steel is basically the superposition of two shapes mentioned *** crack on straightening in continuous casting belongs to intergranular fracture,and the crack on rolling (crack expansion) belongs to transgranular fracture.

关键词： hot ductility crack Nb-containing steel Ti-containing steel