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On c-equivalence

Science China Mathematics 2009年第12期52卷 2389-2396页

作者： LI Xia Department of Mathematics,nanjing university,nanjing 210093,China Department of Mathematics Nanjing University Nanjing China

In this paper,we propose some c-equivalence specifically for autonomous Lagrangian systems and show how to construct connecting orbits in energy surface based on this c-equivalence.

关键词： c-equivalence autonomous Lagrangian systems connecting orbits

L-R smash products for bimodule algebras

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Progress in Natural Science:Materials International 2006年第6期16卷 580-587页

作者： ZHANG Liangyun (Department of Mathematics, nanjing Agricultural university, nanjing 210095, China Department of Mathematics, nanjing university, nanjing 210008, China) Department of Mathematics Nanjing Agricultural University Nanjing 210095 China Department of Mathematics Nanjing U-niversity Nanjing 210008 China

In this paper, we prove that the L-R smash product A(?)H is exactly the twisted smash product A * H if H is a finite dimensional cocommutative Hopf algebra, and give a sufficient and necessary condition for L-R smash products to be bialgebras (Hopf algebras) . For any finite dimensional coquasitriangular Hopf algebra (H,σ), we prove that the L-R smash product H(?)H is semisimple Artinian if H is semisimple and H * is unimodular. In particular, the L-R smash product D(H)* (?)D(H)* semisimple Artinian if the Drin-fel'd double D(H) is semisimple.

关键词： bimodule algebras L-R smash products coquasitriangular Hopf algebras Long bialgebras.

Maschke-type theorem and Morita context over weak Hopf algebras

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Science China Mathematics 2006年第5期49卷 587-598页

作者： ZHANG Liangyun College of Science, nanjing Agricultural university, nanjing 210095, China Department of Mathematics, nanjing university, nanjing 210008, China College of Science Nanjing Agricultural University Nanjing China Department of Mathematics Nanjing University Nanjing China

This paper gives a Maschke-type theorem over semisimple weak Hopf algebras,extends the well-known Maschke-type theorem given by Cohen and Fishman and constructs a Morita context over weak Hopf algebras.

关键词： weak Hopf algebra, smash product, Maschke-type theorem, Morita context.

A Study on the Kunyang Aulacogen

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Acta Geologica Sinica(English Edition) 1991年第2期65卷 131-144页

作者： Hua Renmin nanjing university, nanjing,Jiangsu Province nanjing university Nanjing Jiangsu Province

The Kunyang Aulacogen is a continental rift which initiated at the beginning of the Middle Proterozoic. Itwas generated on the rigid continental crust represented by the crystalline Kangding Complex, and is boundedby two N-S-trending deep faults--Anninghe-Luzhijiang Fault and Xiaojiang Fault. Its early stage of rupturewas characterized by alkalinc mafic igneous activities in the Dahongshan Group and Hekou Group. Duringthe later tensile-depression stage the aulacogen evolved into a graben where scdimentation of the KunyangGroup took place. The sedimentary sequence comprises terrestrial red beds, algal dolomite, marine black shaleand carbonate rocks which are quite typical of rift sedimentary association, and contains stratabound copperdeposits of the well-known Dongchuan type.

关键词： A Study on the Kunyang Aulacogen

A GOLDSTEIN'S TYPE PROJECTION METHOD FOR A CLASSOF VARIANT VARIATIONAL INEQUALITIES

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Journal of Computational Mathematics 1999年第4期17卷 425-434页

作者： Bing-sheng He(Department of Mathematics, nanjing university, nanjing 210008, China) Department of Mathematics Nanjing University Nanjing 210008 China

Some optimization problems in mathematical programming can be translated to a variant variational inequality of the following form: Find a vectoru*, such that This paper presents a simple iterative method for solving this class of variational inequalities. The method can be viewed as an extension of theGoldstein's projection method. Some results of preliminary numerical experiments are given to indicate its applications.

关键词： Variational inequality Goldstein projection method.

HIGH RESOLUTION SCB SCHEME FOR HYPERBOLIC SYSTEMS OF 2-D CONSERVATION LAWS

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Journal of Computational Mathematics 1998年第2期16卷 179-192页

作者： Ning Zhao (Department of Aerodynamics, nanjing university of Aeronautics and Astronautics, nanjing 210016, China) 南京航空航天大学空气动力学系江苏南京

In this paper, a new class of high resolution schemes satisfying the 'condition A' (SCA) and the 'condition B' (SCB) for hyperbolic systems of conservation laws in one and two dimensions are constructed. Moreover, the results of the numerical experiments by using these schemes are given for the system of Euler equations in one and two dimensions.

关键词： SCB scheme hyperbolic system conservation law

GLOBAL CONVERGENCE AND IMPLEMENTATION OF NGTN METHOD FOR SOLVING LARGE-SCALE SMARSE NONLINEAR PROGRAMMING PROBLEMS

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Journal of Computational Mathematics 2001年第4期19卷 337-346页

作者： Qin Ni (Department of Mathematics, nanjing university of Aeronautics and Astronautics, nanjing 210016, China) 南京航空航天大学江苏南京 210016

An NGTN method was proposed for solving large-scale sparse nonlinear programming (NLP) problems. This is a hybrid method of a truncated Newton direction and a modified negative gradient direction, which is suitable for handling sparse data structure and pos sesses Q-quadratic convergence rate. The global convergence of this new method is proved, the convergence rate is further analysed, and the detailed implementation is discussed in this paper. Some numerical tests for solving truss optimization and large sparse problems are reported. The theoretical and numerical results show that the new method is efficient for solving large-scale sparse NLP problems.

关键词： Nonlinear programming Large-scale problem Sparse.

(1.2)INVERSES OF OPERATORS BETWEEN BANACH SPACES AND LOCAL CONJUGACY THEOREM

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Chinese Annals of Mathematics,Series B 1999年第1期20卷 57-62页

作者： MA JIPU(Department of Mathematics,nanjing university,nanjing 210093,China) Department of Mathematics Nanjing University Nanjing 210093 China

1.(1.2)InverseandLocalFinePropertyofaFamilyofOperatorsTxLetEandFbebothBanachspaces,andB(E,F)thesetofallboundedlinearoperatorsfromEintoFAnoperatorT+B(F,E)issaidtobea(1.2)inverseofTifTT+T=TandT+TT+=T+.IfT+satisfiesonlyt... 详细信息

关键词：非线性半弗雷德霍姆映射反转算子巴拿赫空间局部共轭性

Effect of Conversion Efficiency on Gamma-Ray Burst Energy

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Chinese Journal of Astronomy and Astrophysics 2004年第3期4卷 267-274页

作者： Lei Xu Zi-Gao Dai Department of Astronomy nanjing university nanjing 210093 Department of Astronomy Nanjing University Nanjing 210093

Beaming effect makes it possible that gamma-ray bursts have a standardenergy, but the gamma-ray energy release is sensitive to some parameters. Our attention is focusedon the effect of the gamma ray conversion efficiency (η_γ), which may range between 0.01 and 0.9,and which probably has a random value for different GRBs under certain conditions. Making use of theafterglow data from the literature, we carried out a complete correction to the conical openingangle formula. Within the framework of the conical jet model, we ran a simple Monte Carlo simulationfor random values of η_γ, and found that the gamma-ray energy release is narrowly clustered,whether we use a constant value of η_γ or random values for different gamma-ray bursts.

关键词： gamma rays: bursts ISM: jets