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Existence of the solutions and the attractors for the large-scale atmospheric equations

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Science china Earth Sciences 2006年第6期49卷 650-660页

作者： HUANG Haiyang1 & GUO Boling2 1. department of mathematics, beijing Normal University, beijing 100875, china 2. institute of Applied Physics and Computational mathematics, beijing 100080, china department of mathematics Beijing Normal University Beijing China institute of Applied Physics and Computational mathematics Beijing China

In this paper, firstly, the proper function space is chosen, and the proper expression of the operators is introduced such that the complex large-scale atmospheric motion equations can be described by a simple and abstract equation, by which the definition of the weak solution of the atmospheric equations is made. Secondly, the existence of the weak solution for the atmospheric equations and the steady state equations is proved by using the Galerkin method. The existence of the non-empty global attractors for the atmospheric equations in the sense of the Chepyzhov-Vishik’s definition is obtained by constructing a trajectory attractor set of the atmospheric motion equations. The result obtained here is the foundation for studying the topological structure and the dynamical behavior of the atmosphere attractors. Moreover, the methods used here are also valid for studying the other atmospheric motion models.

关键词： atmosphere equations, weak solution, trajectory attractor, global attractor, equilibrium.

CONVERGENCE OF CHORIN-MARSDEN FOR MULA FOR THENAVIER-STOKES EQUATIONS ON CONVEX DOMAINS

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Journal of Computational mathematics 1999年第1期17卷 73-88页

作者： Lung-an Ying(Research institute for Mathematical Sciences, Kyoto University, Japan department of mathematics, Peking University, beijing 100871, china) 北京大学数学系北京

We prove the convergence of the Chorin-Marsden product formula for solving the initial-boundary value problems of the Navier-Stokes equations on convex domains. As a particular case we consider the case of the half pl... 详细信息

关键词： Navier Stokes equation vortex method fractional step method convergence

EXPONENTIAL STABILITY OF A REPARABLE MULTI-STATE DEVICE

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Journal of Systems Science & Complexity 2007年第3期20卷 437-443页

作者： Weiwei HU Houbao XU Jingyuan YU Guangtian ZHU beijing institute of Information and Control Beijing 100037 China. department of mathematics Beijing Institute of Technology Beijing 100081 China. Academy of mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China.

The exponential stability of a multi-state device is discussed in this paper. We present that the Co-semigroup generated by the system operator is quasi-compact and irreducible. It is known that 0 is a simple eigenvalue of the system operator. In combination with this, we obtain that the time-dependent solution exponentially converges to the steady-state solution, which is the positive eigenfuction corresponding to the simple eigenvalue O.

关键词： C0-semigroup exponential stability irreducibility quasi-compact.

Application of Soliton Theory to the Construction of Isometric Immersions of M^(n_1) (c_1)×M^(n_2) (c_2) into Constant Curvature Spaces M^n (±1)

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Acta Mathematica Sinica,English Series 2002年第4期18卷 765-778页

作者： Jian Hua CHEN department of mathematics. Peking University, beijing 100871. P. R. china department, of mathematics, Armored Force Engineering institute, beijing 100072, P. R. china department of mathematics Peking University Beijing P. R. China department of mathematics Armored Force Engineering Institute Beijing P. R. China

In this paper, we apply the soliton theory to the case of isometric immersion in differential geometry and obtain a family of isometric immersions from M^(n1) (c_1)×M^(n2)(c_2) to space forms M^n(c) by introducing 2-... 详细信息

关键词： Soliton theory Isometric immersion Riemaniann product

Tuning surface active oxygen of lanthanum oxide via partial dissolution and regrowth of crystallites

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Journal of Natural Gas Chemistry 2011年第5期20卷 483-486页

作者： Zhiming Gao, Huili Li Key Laboratory of Cluster Science, Ministry of Education of china department of Chemistry, School of Science, beijing institute of technology, beijing 100081, china Key Laboratory of Cluster Science Ministry of Education of China department of Chemistry School of Science Beijing Institute of Technology Beijing 100081 China

A commercial lanthanum oxide was modified into X%-La2O3 samples via partial dissolution and regrowth of crystallites, wherein the X value denotes the weight percent of the initial metal oxide powder dissolved by nitric acid. BET measurements and TEM observations indicate that the 20%-La2O3 sample has an increased specific surface area, relatively thin and small crystallites in size. TPD/TPR profiles also show that the 20%-La2O3 sample has more surface active oxygen than the 0%-La2O3 sample. Among the four X%-La2O3 samples, the highest activity for methane oxidation was obtained over the 20%-La2O3 sample. Therefore, the present work proves that the method of partial dissolution and regrowth of crystallites are effective to modify surface property of lanthanum oxide.

关键词： solid state reaction surface oxygen crystallite regrowth TPR metal oxide

The Existence of Solutions to Sturm-Liouville Boundary Value Problems with Laplacian-like Operator

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Acta Mathematicae Applicatae Sinica 2002年第2期18卷 341-348页

作者： Wei-ping Sun, Wei-gao Gedepartment of Applied mathematics, beijing institute of technology, beijing 100081, china department of Applied mathematics Beijing Institute of Technology Beijing China

The existence of infinitely many solutions to Sturm-Liouville boundary value problem with a Laplacian-like operator is studied by applying generalized polar coordinates.

关键词： Generalized polar coordinates Laplacian-like operator boundary value problem

Complex variable method for plane elasticity of icosahedral quasicrystals and elliptic notch problem

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Science china(Physics,Mechanics & Astronomy) 2008年第7期51卷 773-780页

作者： LI LianHe1,2 & FAN TianYou1 1 department of Physics, beijing institute of technology, beijing 100081, china 2 College of mathematics Science, Inner Mongolia Normal University, Hohhot 010022, china department of Physics Beijing Institute of Technology Beijing China College of mathematics Science Inner Mongolia Normal University Hohhot China

The complex variable method for the plane elasticity theory of icosahedral quasicrystals is developed. Based on the general solution obtained previously, complex representations of stress and displacement components of phonon and phason fields in the quasicrystals are given. With the help of conformal transformation, an analytic solution for the elliptic notch problem of the material is presented. The solution of the Griffith crack problem can be observed as a special case of the results. The stress intensity factor and energy release rate of the crack are also obtained.

关键词： icosahedral quasicrystals plane elasticity elliptic notch complex variable method

On the coupled NBEM and FEM for a class of nonlinear exterior Dirichlet problem in R^(2*)

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Science china mathematics 2004年第Z1期47卷 181-189页

作者： WU Zhengpeng, KANG Tong & YU Dehaoinstitute of Computational mathematics and Scientific/Engineering Computing, Academy of mathematics and System Sciences, Chinese Academy of Sciences, beijing 100080, china department of Applied mathematics, beijing Broadcasting institute, beijing 100024, china Combinatorial and Computational mathematics Center, Pohang University of Science and technology, Phoang 790-784, Republic of Korea institute of Computational mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China department of Applied mathematics Beijing Broadcasting Institute Beijing China Combinatorial and Computational mathematics Center Pohang University of Science and Technology Phoang Republic of Korea

In this paper, based on the natural boundary reduction advanced by Feng and Yu, we couple the finite elementapproach with the natural boundary element method to study theweak solvability and Galerkin approximation of a class ofnonlinear exterior boundary value problems. The analysis is mainlybased on the variational formulation with *** provethe error estimate of the finite element solution and obtain theasymptotic rate of convergence. Finally, we also give anumerical example.

关键词： natural boundary integral method, finite element method, coupling method, error estimate.

Multi-parameter infinite-dimensional(r,δ)-OU process

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Chinese Science Bulletin 1999年第5期44卷 418-423页

作者： WANG Zikuninstitute of mathematics, Shantou University, Shantou 515063, china department of mathematics, beijing Normal University, beijing 100875, china institute of mathematics Shantou University Shantou China department of mathematics Beijing Normal University Beijing China

The definition of n-parameter infinite-dimensional (r, δ) -Ornstein-Uhlenbeck process {X_t (·)}((r,δ)-OUP_n~∞ for short) is given. The absolute continuity of distribution μ_t of X_t(·) and the limit of X_t(·) w... 详细信息

关键词： multi-parameter (r δ)-OUPn∞ absolute continuity in hierarchy.