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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 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) (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 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

An Underwater Biomimetic Robot that can Swim,Bipedal Walk and Grasp

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Journal of Bionic Engineering 2024年第3期21卷 1223-1237页

作者： Qiuxuan Wu Liwei Pan FuLin du ZhaoSheng Wu XiaoNi Chi FaRong Gao jian wang Anton A.Zhilenkov School of Automation Hangzhou Dianzi UniversityHangzhou310018China International Joint Research Laboratory for Autonomous Robotic Systems Hangzhou310018China GEELY Automotive Institute Hangzhou Vocational and Technical CollegeHangzhou310018China Institute of Hydrodynamics and Control Processes Sankt-Petersburg Saint Petersburg State Marine Technical UniversitySankt-PetersburgRussia

In developing and exploring extreme and harsh underwater environments,underwater robots can effectively replace humans to complete *** meet the requirements of underwater flexible motion and comprehensive subsea operation,a novel octopus-inspired robot with eight soft limbs was designed and *** robot possesses the capabilities of underwater bipedal walking,multi-arm swimming,and grasping *** closely interact with the underwater seabed environment and minimize disturbance,the robot employs a cable-driven flexible arm for its walking in underwater floor through a bipedal walking *** multi-arm swimming offers a means of three-dimensional spatial movement,allowing the robot to swiftly explore and navigate over large areas,thereby enhancing its ***,the robot’s walking arm enables it to grasp and transport objects underwater,thereby enhancing its practicality in underwater environments.A simplified motion models and gait generation strategies were proposed for two modes of robot locomotion:swimming and walking,inspired by the movement characteristics of octopus-inspired multi-arm swimming and bipedal *** experimental verification,the robot’s average speed of underwater bipedal walking reaches 7.26 cm/s,while the horizontal movement speed for multi-arm swimming is 8.6 cm/s.

关键词： Underwater soft robots Underwater bipedal walking Multi-arm swimming Cable drive

Research status of hormone replacement therapy on mood and sleep quality in menopausal women

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World Journal of Psychiatry 2024年第9期14卷 1289-1293页

作者： Xue-jian wang Department of Neurosurgery Affiliated Hospital 2 of Nantong UniversityNantong 226000Jiangsu ProvinceChina

Menopausal syndrome is a common disease of clinical women,which refers to a series of physical and mental symptoms caused by the fluctuation or reduction of sex hormones before and after *** of these patients have sleep and mood abnormalities that affect their health and quality of *** present,the understanding of it is gradually *** paper mainly analyzes its back-ground and current treatment.

关键词： Effects Hormone replacement therapy Menopause Women Mood states Sleep quality Sex hormones

Trend of Storm Surge Induced by Typical Landfall Super Typhoons during 1975–2021 in the Eastern china Sea

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Journal of Ocean University of china 2024年第2期23卷 277-286页

作者： LUO Feng wang Yi TAO Aifeng SHI jian wang Yongzhi ZHANG Chi college of Harbour Coastal and Offshore EngineeringHohai UniversityNanjing 210098China nantong Ocean and Coastal Engineering Research Institute Hohai UniversityNantong 226000China Key Laboratory of Ministry of Education for Coastal Disaster and Protection Hohai UniversityNanjing 210098China college of Meteorology and Oceanography National University of Defense TechnologyChangsha 410073China The First Institute of Oceanography MNRQingdao 266061China

Climate change affects the activity of global and regional tropical cyclones(TCs).Among all TCs,typical super typhoons(STYs)are particularly devastating because they maintain their intensity when landing on the coast and thus cause casualties,economic losses,and environmental *** a 3D tidal model,we reconstructed the typhoon(TY)wind field to simulate the storm surge induced by typical *** TY activity was then analyzed using historical *** showed a downtrend of varying degrees in the annual frequency of STYs and TCs in the Western North Pacific(WNP)Basin,with a significant trend change observed for TCs from 1949 to 2021.A large difference in the interannual change in frequency was found between STYs and TCs in the WNP and Eastern china Sea(ECS).Along the coast of EC,the frequency of landfall TCs showed a weak downtrend,and the typical STYs showed reverse micro growth with peak activity in ***,Fujian,and Taiwan were highly vulnerable to the frontal hits of typical *** by climate change,the average lifetime maximum intensity(LMI)locations and landfall locations of typical STYs in the ECS basin showed a significant poleward migration *** addition,the annual average LMI and accumulated cyclone energy showed an uptrend,indicating the increasing severity of the disaster *** by the typical STY activity in the ECS,the maximum storm surge area also showed poleward migration,and the coast of North china faced potential growth in high storm surge risks.

关键词： storm surge super typhoons tropical cyclones eastern china Sea poleward migration

Analysis of the Flow Field and Impact Force in High-Pressure Water Descaling

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Fluid Dynamics & Materials Processing 2024年第1期20卷 165-177页

作者： Yue Cui Liyuan wang jian Wu Haisheng Liu Di Wu Key Lab of Intelligent Equipment Digital Design and Process Simulation Hebei ProvinceTangshan UniversityTangshan063000China Department of Intelligent Manufacturing Tangshan Vocational College of Science and TechnologyTangshan063001China

This study aims to improve the performances of the high-pressure water descaling technology used in steel hot rolling *** particular,a 2050 mm hot rolling line is considered,and the problem is investigated by means of a fluid–structure interaction(FSI)method by which the descaling effect produced by rolling coils with different section sizes is *** a flat fan-shaped nozzle at the entrance of the R1R2 roughing mill,the outflow field characteristics and the velocity distribution curve on the strike line(at a target distance of 30–120 mm)are *** is found that the velocity in the center region of the water jet with different target distances is higher than that in the boundary *** the target distance increases,the velocity of the water jet in the central region *** comparison with experimental results,it is shown that the simulation model can accurately predict the impact position of the high-pressure water on the impact plate,thereby providing a computational scheme that can be used to optimize the nozzle space layout and improve the slabs’descent effect for different rolling specifications.

关键词： High pressure water descaling flow field analysis FSI target distance strike range

Star-factorization of the Complete Bipartite Multigraphs

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Acta Mathematicae Applicatae Sinica 2023年第2期39卷 239-248页

作者： Jing SHI jian wang bei-liang du School of Science Nantong UniversityNantong 226007China Department of Mathematics Suzhou UniversitySuzhou 215006China Mathematics Teaching and Research Office Nantong Vocational CollegeNantong 226007China

LetλK_(m,n)be a complete bipartite multigraph with two partite sets having m and n vertices,respectively.A K_(p,q)-factorization ofλK_(m,n)is a set of K_(p,q)-factors ofλK_(m,n)which partition the set of edges ofλK_(m,n).Whenλ=1,Martin,in[Complete bipartite factorizations by complete bipartite graphs,Discrete Math.,167/168(1997),461–480],gave simple necessary conditions for such a factorization to exist,and conjectured those conditions are always *** this paper,we will study the K_(p,q)-factorization ofλK_(m,n)for p=1,to show that the necessary conditions for such a factorization are always sufficient whenever related parameters are sufficiently large.

关键词： complete bipartite multigraph star factorization