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On homotopy regular monomorphisms

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Chinese Science Bulletin 1998年第1期43卷 27-30页

作者： CHEN Jixiang department of mathematics, Nankai university, tianjin 300071, china department of mathematics Nankai University Tianjin China

A concept of homotopy regular monomorphism is introduced which is strictly between homotopy monomorphism and homotopy equivalence. And it characterizes homotopy equivalence in some sense.

关键词： homotopy monomorphism homotopy equalizer homotopy regular monomorphism homotopy pull back.

THE STABILITY OF THE PERIODIC SOLUTIONS OF SECOND ORDER HAMILTONIAN SYSTEMS

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Chinese Annals of mathematics,Series B 2000年第2期21卷 225-232页

作者： LIU CHUNGEN(department of mathematics, Nankai university, tianjin 300071, china.) department of mathematics Nankai University Tianjin 300071 China

This paper studies the stability of the periodic solutions of the second order Hamiltonian systems with even superquadratic or subquadratic potentials. The author proves that in the subquadratic case, there exist infinite geometrically distinct elliptic periodic solutions, and in the superquadratic case, there exist infinite geometrically distinct periodic solutions with at most one instability direction if they are half period non-degenerate, otherwise they are elliptic.

关键词：稳定性周期解哈密顿系统位势

Optimal value functions of generalized semi-infinite min-max programming on a noncompact set

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Science china mathematics 2005年第2期48卷 261-276页

作者： WANG Changyu, YANG Xiaoqi & YANG Xinmin Institute oi Operations Research, Qufu Normal university, Qufu 273165, china department of applied mathematics, Dalian university of technology, Dalian 116024, china department of applied mathematics, The Hong Kong Polytechnic university, Hong Kong, china department of mathematics, Chongqing Normal university, Chongqing 400047, china Institute of Operations Research Qufu Normal University Qufu China department of applied mathematics Dalian University of Technology Dalian China department of applied mathematics The Hong Kong Polytechnic University Hong Kong China department of mathematics Chongqing Normal University Chongqing China

In this paper, we study optimal value functions of generalized semi-infinite min-max programming problems on a noncompact set. Directional derivatives and subdifferential characterizations of optimal value functions are given. Using these properties,we establish first order optimality conditions for unconstrained generalized semi-infinite programming problems.

关键词： optimal value function, directional derivative, subdifferential, semi-infinite programming, first order optimality condition.

STRONG LAW OF LARGE NUMBERS AND SHANNON-MCMILLAN THEOREM FOR MARKOV CHAINS FIELD ON CAYLEY TREE

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Acta Mathematica Scientia 2001年第4期21卷 495-502页

作者：杨卫国刘文 Faculty of Science Jiangsu University of Science and Technology Zhenjiang 212013 China hebei university of technology Tianjin 300130 China

This paper studies the strong law of large numbers and the Shannom-McMillan theorem for Markov chains field on Cayley tree. The authors first prove the strong law of large number on the frequencies of states and orderd couples of states for Markov chains field on Cayley tree. Then they prove the Shannon-McMillan theorem with a.e. convergence for Markov chains field on Cayley tree. In the proof, a new technique in the study the strong limit theorem in probability theory is applied.

关键词： Cayley tree random field Markov chains field strong law of large numbers Shannon-McMillan theorem

Low－Temperature　Spectral　Properties　and　Zero－Phonon　Transitions　of　Alkali　Halide　Crystal　Materials　Bombarded　with　Electrons　and　Implanted　with　Ions

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Chinese Journal of Lasers 1995年第2期B4卷 111-116页

作者： GU Hongen(department of applied Physics, tianjin university, tianjin 300072, china) tianjin Univ Tianjin China

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关键词： zero-phonon transition. color centers

PRIMAL PERTURBATION SIMPLEX ALGORITHMS FOR LINEAR PROGRAMMING

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Journal of Computational mathematics 2000年第6期18卷 587-596页

作者： Ping-qi Pan (department of applied mathematics, Southeast university, Nanjing 210096, china.) 东南大学江苏南京 210096

In this paper, we propose two new perturbation simplex variants. Solving linear programming problems without introducing artificial variables, each of the two uses the dual pivot rule to achieve primal feasibility, and then the primal pivot rule to achieve optimality. The second algorithm, a modification of the first, is designed to handle highly degenerate problems more efficiently. Some interesting results concerning merit of the perturbation are established. Numerical results from preliminary tests are also reported. [ABSTRACT FROM AUTHOR]

关键词： linear programming perturbation primal simplex algorithm partially revised tableau

Transition prediction for supersonic and hypersonic boundary layers on a cone with angle of attack

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Science china(Physics,Mechanics & Astronomy) 2009年第8期52卷 1223-1232页

作者： SU CaiHong1 & ZHOU Heng1,2 1 department of Mechanics,tianjin university,tianjin 300072,china 2 Liu-Hui Center of applied mathematics,Nankai university and tianjin university,tianjin 300072,china department of Mechanics Tianjin University Tianjin China Liu-Hui Center of applied mathematics Nankai University and Tianjin University Tianjin China

Transition prediction for boundary layers has always been one of the urgent problems waiting for a solution for the development of aero-space technology,yet there is no reliable and effective method due to the complexity of the *** eN method has been regarded as an effective method for the transition prediction of boundary ***,it heavily relies on experiment or *** in cases with three-dimensional base flow,for instance,the boundary layer on a cone with angle of attack,the result of its application is not *** authors have found its cause and proposed the method for its improvement,which did yield the fairly satisfactory result for a given test case,and also did not rely so much on experiment or ***,before people can really apply this method to practical problems,more test cases have to be *** this paper,more test cases for the application of the improved eN method to problems of transition prediction of supersonic and hypersonic boundary layers on cones with angle of attack will be *** results are compared with those obtained by experiments and/or direct numerical simulations,confirming that the improved eN method is effective and *** also find that there may be more than one ZARF for each meridian plane,and which one should be chosen for the eN method has been clarified.

关键词： angle of attack cone boundary layer transition eN method

Convergence of Hermite interpolatory operators

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Science china mathematics 2010年第8期53卷 2115-2126页

作者： LIU YouMing & ZHAO JunJian department of applied mathematics,Beijing university of technology,Beijing 100124,china department of applied mathematics Beijing University of Technology Beijing China

Divergence-free wavelets play important roles in both partial differential equations and fluid *** constructions of those wavelets depend usually on Hermite *** study several types of convergence of the related Hermite interpolatory operators in this *** precisely,the uniform convergence is firstly discussed in the second part;then,the third section provides the convergence in the Donoho's *** on these results,the last two parts are devoted to show the convergence in some Besov spaces,which concludes the completeness of Bittner and Urban's expansions.

关键词： Besov spaces Hermite splines convergence completeness

THE FULL DISCRETE DISCONTINUOUS FINITE ELEMENT ANALYSIS FOR FIRST-ORDER LINEAR HYPERBOLICEQUATION

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Journal of Computational mathematics 1999年第1期17卷 97-112页

作者： Che Sun Shu-jie Qin(department of mathematics, Nankai university, tianjin 300071, china) department of mathematics Nankai University Tianjin 300071 China

In this paper, the full discrete discontinuous Galerkin finite element method to solove 2-dimensional first-order linear hyperbolic problem is considered. Two practical schemes, Euler scheme and Crank-Nicolson scheme, are constructed. For each of them, the stability and error estimation with optimal order approximation is established in the norm stronger than L-2-norm.

关键词： hyperbolic equation discontinuous FEM Euler scheme