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ON THE VARIATIONS OF G_2

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chinese Annals of mathematics,Series B 2003年第3期24卷 387-394页

作者： LIU DONG LIN LEI department of mathematics, East c.ina Normal university, shanghai 200062, c.ina. department of mathematics, East c.ina Normal university, shanghai 200062, c.ina. department of mathematics East China Normal University Shanghai 200062 China

In [1], Shen Guangyu constructed several classes of new simple Lie algebras of characteristic 2, which are called the variations of G2. In this paper, the authors investigate their derivation algebras. It is shown that G2 and its variations all possess unique nondegenerate associative forms. The authors also find some nonsingular derivations of ViG for i = 3,4, 5, 6, and thereby construct some left-symmetric structures on Vi G for i = 3,4,5,6. Some errors about the variations of sl(3, F) in [1] are corrected.

关键词： Variation Derivation Associative form Left-symmetric structure

STEADY-STATE SOLUTIONS FOR A ONE-DIMENSIONAL NONISENTROPIc HYDRODYNAMIc MODEL WITH NON-cONSTANT LATTIcE TEMPERATURE

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Acta Mathematica Scientia 2008年第3期28卷 479-488页

作者：黎野平 department of mathematics Xianning College

A one-dimensional stationary nonisentropic hydrodynamic model for semiconductor devices with non-constant lattice temperature is studied. This model consists of the equations for the electron density, the electron current density and electron temperature, coupled with the Poisson equation of the electrostatic potential in a bounded interval supplemented with proper boundary conditions. The existence and uniqueness of a strong subsonic steady-state solution with positive particle density and positive temperature is established. The proof is based on the fixed-point arguments, the Stampacchia truncation methods, and the basic energy estimates.

关键词： Steady-state nonisentropic hydrodynamic model semiconductor subsonic

BLOcKWISE PERTURBATION THEORY FOR 2×2 BLOcK MARKOV cHAINS

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Journal of computational mathematics 2000年第3期18卷 305-312页

作者： Jun-gong Xue Wei-guo Gao (department of mathematics, Fudan university, shanghai, 200433, c.ina) 复旦大学上海 200433

Let P be a transition matrix of a Markov chain and be of the form P = qq@. The stationary distribution πT is partitioned conformally in the form (π1T, π2T). This paper establish the relative error bound in πiT (i ... 详细信息

关键词： Blockwise perturbation Markov chains stationary distribution error bound

THE INVARIANT cONTINUOUS-TRAcE c*-ALGEBRAS BY THE AcTIONS OF cOMPAcT ABELIAN GROUPS

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chinese Annals of mathematics,Series B 1998年第4期19卷 489-498页

作者： FANG XIAOcHUN (department of Applied mathematics, Tonaii university, shanghai, 200092, c.ina.) Tongji Univ Dept Appl Math Shanghai 200092 Peoples R China

The author studies the relation of continuous-trace property between c*-algebra A and the fixed point c*-algebra Aα in certain c*-dynamic system (A, G, α) by introducing an α-invariant　continuous trace property. For separable c*-dynamic system (A, G, α) with G compact and　abelian,A liminal, αt ∈ Autcb(A) (A) and pointwise unitary, the necessary and sufficient condition for A to be continuous-trace, which contains Aα continuousitrace, is obtained.

关键词： continuous-Trace Action of Group c*-Algebra

The Geometric Structure of Strange Attractors in the Lozi Map

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communications in Nonlinear Science and Numerical Simulation 1998年第2期3卷 67-71页

作者： Yongluo cAO and Zengrong LIU* (department of mathematics, Suzhou university,Suzhou 215006, c.ina) *(department of mathematics, shanghai university,shanghai 200072, c.ina) (E mail: ***) department of mathematics Suzhou University Suzhou 215006 China department of mathematics Shanghai University Shanghai 200072 China

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ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｅｐａｓｔｔｗｏｄｅｃａｄｅｓ，ｔｈｅｓｔｒａｎｇｅａｔｒａｃｔｏｒｓｉｎｔｈｅｆｉｅｌｄｏｆｎｏｎｌｉｎｅａｒｓｃｉｅｎｃｅｄｒａｗｓｔｈｅａｔｅｎｔｉｏｎｏｆｍａｎｙｓｃｉｅｎｔｉｓｔｓ．Ｉｎｐａｒｔｉｃｕｌａｒ，...

关键词： strange attractor transversal homoclinic point weak transversal homoclinic point

A THEOREM ON PLURIcANONIcAL MAPS OF NONSINGULAR MINIMAL THREEFOLDS OF GENERAL TYPE

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chinese Annals of mathematics,Series B 1998年第4期19卷 415-420页

作者： cHEN MENG (department of mathematics, TOng n university, shanghai 200092, c.ina.) Tongji Univ Dept Math Shanghai 200092 Peoples R China

Let X be a complex nonsingular projective threefold of general type. It is shown that the dimension of the image of X through m-canonical maps is at least two for every m 3.

关键词： Minimal model Pluricanonical map composed of a pencil

ON NON-ISOTROPIc JAcOBI PSEUDOSPEcTRAL METHOD

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Journal of computational mathematics 2008年第4期26卷 511-535页

作者： Benyu Guo Keji Zhang department of mathematics,shanghai Normal university,shanghai 200234,c.ina Scientific computing Key Laboratory of shanghai Universities Division of computational Science of E-Institute of shanghai Universities department of mathematics Shanghai Normal University Shanghai 200234

In this paper, a non-isotropic Jacobi pseudospectral method is proposed and its appli- cations are considered. Some results on the multi-dimensional Jacobi-Gauss type interpolation and the related Bernstein-Jackson type inequalities are established, which play an important role in pseudospectral method. The pseudospectral method is applied to a twodimensional singular problem and a problem on axisymmetric domain. The convergence of proposed schemes is established. Numerical results demonstrate the efficiency of the proposed method.

关键词： Jacobi pseudospectral method in multiple dimensions Jacobi-Gauss type inter-polation Bernstein-Jackson type inequalities Singular problem Problem on axisymmetricdomain.

Optimal motion planning of an underactuated spacecraft using wavelet approximate method

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Progress in Natural Science:Materials International 2006年第8期16卷 868-873页

作者： GE Xinsheng, cHEN Liqun and LIU Yanzhu (Beijing Institute of Machinery, Beijing 100085, c.ina department of Mechanics, shanghai university, shanghai 200072, c.ina department of Engineering Mechanics, shanghai jiaotong university, shanghai 200030, c.ina) [a]Beijing Institute of Machiner Beijing China [b]department of Mechanics Shanghai University Shanghai China [c]department of Engineering Mechanics Shanghai Jiaotong University Shanghai China

An optimal motion planning scheme using wavelet approximation is proposed for an underactuated spacecraft. The motion planning of an underactuated spacecraft can be formulated as an optimal control of a drift-free system. A cost functional is used to incorporate the control energy and the final state errors. The motion planning is to determine control inputs to minimize the cost functional. Using the method of wavelet, one can transform an infinite-dimensional optimal control problem to a finite-dimensional one and use Gauss-Newton algorithm to solve it for a feasible trajectory which satisfies nonholonomic constraints. The proposed scheme has been applied to a rigid spacecraft with two momentum wheels. The numerical simulation results indicate that optimal control with wavelet approximation is an effective approach to steering an underactuated spacecraft system from the initial configuration to the final configuration.

关键词： underactuated spacecraft motion planning optimal control nonholonomic constraint wavelet analysis.

JAcOBI SPEcTRAL APPROXIMATIONS TO DIFFERENTIALEQUATIONS ON THE HALF LINE

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Journal of computational mathematics 2000年第1期18卷 95-112页

作者： Ben-yu Guo(department of mathematics, shanghai Normal university, shanghai 200234, c.ina)(cOM2MAc, Pohang university of Science and Technology, Pohang, Korea) 上海师范大学上海 200234

Presents a study which investigated some Jacobi approximations which are used for numerical solutions of differential equations on the half line. Application of the approximations to problems on unbounded domains; Alg... 详细信息

关键词： Jacobi spectral approximations differential equations on the half line stability and convergence