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Science China Mathematics 2007年第8期50卷 1205-1216页

作者： Zai-hong WANG School of Mathematical Sciences,Capital Normal University,Beijing 100037,China School of Mathematical Sciences Capital Normal University Beijing China

In this paper,we deal with the existence of unbounded orbits of the mapping where n is a positive integer,c is a constant andμ（θ）is a 2π-periodic function.We prove that if c>0 andμ（θ）≠0,θ∈[0,2π],then every orbit of the given mapping goes to infinity in the future forρlarge enough;if c+-bx-+φ（x）= p（t）has unbounded solutions provided that a,b satisfy 1/a1/2+1/b1/2=2/n and F（x）（=∫0x f（s）ds）, andφ（x）satisfies some limit conditions.At the same time,we obtain the existence of 2π-periodic solutions of this equation.

关键词： Liénard equations unbounded solutions periodic solutions

The multi-soliton solutions of the CH-γ equation

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Science China Mathematics 2008年第2期51卷 314-320页

作者： CHEN ChunLi~(1+) LI YiShen~2 ZHANG JinE~3 1 Department of Mathematics,Shanghai Jiaotong University,Shanghai 200240,China 2 Department of Mathematics,University of Science and Technology of China,Hefei 230026,China 3 SB and SEF,University of Hong Kong,Pokfulam Road,Hong Kong,China Department of Mathematics Shanghai Jiaotong University Shanghai China Department of Mathematics University of Science and Technology of China Hefei China SB and SEF University of Hong Kong Hong Kong China

This paper solves the integrable CH-γequation for analytical multiple soliton solutions with the Darboux transformation method.Some properties of the soliton solutions are different from the CH equation.

关键词： CH-γequation multi-soliton solutions Darboux transformation

Almost periodic solutions of difference systems

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Chinese Science Bulletin 1998年第24期43卷 2041-2046页

作者： ZHANG Shunian Department of Applied Mathematics, Shanghai Jiaotong University, Shanghai 200240, China Department of Applied Mathematics Shanghai Jiaotong University Shanghai China

For linear difference systems, a rather general result on the existence of almost periodic solutions is established, which also gives the explicit expression of the almost periodic solution in terms of the coefficient matrix and the nonhomogeneous term. The obtained result confirms not only the existence, but also the uniqueness as well as the uniform asymptotic stability of the almost periodic solution. As an application, a criterion on the existence of almost periodic solutions of the second order difference equations is derived.

关键词： difference systems mean values of almost periodic sequences almost periodic solutions existence uniqueness uniform asymptotic stability

Regularity of viscosity solutions near KAM torus

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Science China Mathematics 2008年第3期51卷 361-368页

作者： LIANG ZhenGuo YAN Jun School of Mathematical Sciences and Key Lab of Mathematics for Nonlinear Science Fudan UniversityShanghai 200433China

In this paper, we give weak regularity theorems on P of u~ε(x, P), where u~ε(x, P)is the viscosity solution of the cell problem H_ε(P+D_xu~ε, x)=H_ε(P).

关键词： viscosity solutions KAM torus Hamilton-Jacobi equation

Entire solutions in a delayed nonlocal dispersal competitive system

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International Journal of Biomathematics 2019年第4期12卷 55-78页

作者： Yang Wang Guirong Liu Xiong Li School of Mathematical Sciences Shanxi University Taiyuan 030006P. R.China School of Mathematical Sciences Beijing Normal University Beijing 100875 P. R.China

In this paper, we are concerned with the existence of an entire solution in a delayed nonlocal dispersal competitive system. This entire solution converges to two monotone fronts with different speeds, which approach each other from both sides of the x-axis, as t converge to-∞ and then converge to (1,0) as t converges to +∞. Its global dynamic shows the superior species invade the inferior ones from both sides of the x-axis and then the inferior ones become extinct, which is a new invading way. In fact, our conclusions extend this invading way into a more general competitive system. Furthermore, we show several properties of this entire solution.

关键词： Entire solutions traveling front solutions nonlocal diffusion systems

THERMODYNAMIC PROPERTIES OF Al-Ce-Pb(or Sn) LIQUID solutions

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中国有色金属学会会刊：英文版 1993年第3期3卷 27-28,51页

作者： Sun, Yunyong Du, Ting Central Iron and Steel Research Institute, Beijing 100081, China

Thermodynamic properties of Al-Ce-Pb and Al-Ce-Sn liquid systems were studied by direct equilibrium method at 800℃. The results obtained include: equilibrium products, their standard Gibbs energies of formation, equi... 详细信息

关键词： aluminum-base solutions cerium lead tin thermodynamic properties

Boundedness of solutions and existence of invariant tori for generalized pendulum type equation

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Chinese Science Bulletin 1997年第20期42卷 1673-1675页

作者： HUANG Hai and YUAN Rong1. Institute of Mathematics, Chinese Academy of Sciences, Beijing 100080, China 2. Department of Mathematics, Beijing Normal University, Beijing 100875, China Institute of Mathematics Chinese Academy of Sciences Beijing China Department of Mathematics Beijing Normal University Beijing China

MOTIVATED by various significant applications to non-Newtonian fluid theory, diffusion offlows in porous media, nonlinear elasticity, and theory of capillary surfaces, several authors(see refs.[1,2] and references cited therein ) have recently studied the existence of periodicsolutions and other properties for the following differential equation:

关键词： boundeduess of solutions invariant tori quasiperlodic solutions Moser’s small twist theorem.

Thermodynamics of Cu-Ce-M(M=Sn,Zn,Pb)liquid solutions

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中国有色金属学会会刊：英文版 1994年第3期4卷 17-20页

作者： Du, Ting Li, Guodong(Central Iron and Steel Research Institute Ministry of Metallurgical Industry ,Beijing 100081)

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ＴＨＥＲＭＯＤＹＮＡＭＩＣＳＯＦＣｕ－Ｃｅ－Ｍ（Ｍ＝Ｓｎ，Ｚｎ，Ｐｂ）ＬＩＱＵＩＤＳＯＬＵＴＩＯＮＳＤｕ，Ｔｉｎｇ；Ｌｉ，Ｇｕｏｄｏｎｇ（ＣｅｎｔｒａｌＩｒｏｎａｎｄＳｔｅｅｌＲｅｓｅａｒｃｈＩｎｓｔｉｔｕｔｅＭｉｎｉｓｔｒｙｏｆＭｅｔａｌｌｕｒｇｉ...

关键词： Cu-Ce-M(M=Sn Zn Pb) liquid solutions thermodynamic properties

Accuracy of Lax-Wendroff scheme for discontinuous solutions of convection equations

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Chinese Science Bulletin 1997年第24期42卷 2047-2051页

作者： DING LijuanDepartment of Applied Mathematics, Beijing Institute of Technology, Beijing 100081, China Department of Applied Mathematics Beijing Institute of Technology Beijing China

IT is known from Brenner, Thomee and Wahlbin that the well-known second-order Lax-Wendroff scheme is stable in L^2, but unstable in L^p, p≠2. Generally speaking, if the initialdata is smooth enough and if a difference scheme, which is stable in L^p for some p, has orderof accuracy μ, then we can expect that the solution of the difference scheme converges to thesolution of the differential equation at the rate of order μ in L^p. But for discontinuous solu-tions, which are essential to hyperbolic equations, the above expectation is not true. Error es-timates for discontinuous solutions not only have theoretical meaning, but also practical value.

关键词： Lax-Wendroff scheme modlfled equation discontinuous solutions error estimate.

Study on the Characteristics of Macromolecular Chains of Cellulose in Dilute solutions

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Journal of China Textile University(English Edition) 1999年第3期16卷 21-24页

作者：鲁平陈自力田原刘兆峰 China Textile Univ Shanghai China

The characteristics of macromolecular chains of cellulose in dilute solutions are discussed. Viscometry was used for the measurement of the intrinsic viscosity [η] of four cellulose samples, which were respectively dissolved in the solvent Tri-ethylenediamine cadmium hydroxide Cadoxen (Cadoxen), Cupriethylenediamine hydroxide(Cuen), iron sodium tartrate complex(EWNN) and N,N-dimethylacetamide(DMAc)with lithium chloride(LiCI, 9% w/w). The intrinsic viscosity of the four solutions decreased in the following manner:[η]DMAc/LiCl>[η]EWNN>[η]Cuen>[η]Cadoxen. The stability of cellulose (Sample α-cellulose) dissolved in solvents Cuen and EWNN was tested by plotting the intrinsic viscosity vs. time. The values of Huggins constant K_H for the cellulose samples dissolved in solvents Cadoxen,Cuen,EWNN and DMAc/LiCl (9% w/w ) were calculated.

关键词： cellulose intrinsic viscosity dilute solutions macromolecular chains .