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Fredholm operators in Toeplitz algebras associated with discrete abelian groups

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Chinese Science Bulletin 1998年第14期43卷 1175-1179页

作者： XU Qingxiang 1 and CHEN Xiaoman 2.1. Department of mathematics, shanghai Normal {2., shanghai 2.02.4, china 2. Laboratory of mathematics for Nonlinear Sciences and Institute of mathematics, fudan university, shanghai 2.0433, china Department of mathematics Shanghai Normal University Shanghai China Laboratory of mathematics for Nonlinear Sciences and Institute of mathematics Fudan University Shanghai China

The locally finite below sets are introduced and the Fredholm operators in Toeplitz algebras associated with discrete abelian groups are studied.

关键词： discrete abelian group quasi_ordered group Toeplitz operator Fredholm operator.

THE MODULI SPACE OF COMPLEX LAGRANGIAN SUBMANIFOLDS IN THE HYPER-KAEHLER MANIFOLD

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Chinese Annals of mathematics,Series B 1999年第4期20卷 393-400页

作者： FU JIXIANG(Institute of mathematics, fudan university,{2., china) fudan Univ Inst Math Shanghai 200433 Peoples R China

The deformation of a compact complex Lagrangian submanifold in a hyper-Kaehler manifold and the moduli space are studied. It is proved that the moduli space Mc1 is a special Kaehler manifold, where special means that there is a real flat torsionfree symplectic connection satisfying dI = 0 (I is a complex structure of Mcl). Thus, following [4], one knows thatT*Mcl is a hyper-Kaehler manifold and then that Mcl is a complex Lagrangian submanifold in T* Mcl.

关键词： Moduli space Complex Lagrangian submanifold Hyper-Kaehler manifold Special Lagrangian submanifold Special Kaehler manifold Deformation

THE OCCUPATION DENSITY FIELD FOR THE CATALYTIC SUPER-BROWNIAN MOTION

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Chinese Annals of mathematics,Series B 1999年第4期20卷 447-454页

作者： HONG WENMING(Institute of mathematics, fudan university{2., china) fudan Univ Inst Math Shanghai 200433 Peoples R China

It is proved that the occupation time of the catalytic super-Brownian motion is absolutely continuous for d = 1, and the occupation density field is jointly continuous and jointly Holder continuous.

关键词： Branching rate functional Brownian collision local time Catalytic super-Brownian motion Occupation time Occupation density field

TOTAL GENERALIZED MINIMUM BACKWARD ERROR ALGORITHM FOR SOLVING NONSYMMETRIC LINEAR SYSTEMS

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Journal of Computational mathematics 1998年第6期16卷 539-550页

作者： Zhi-hao Cao (Dearptment of mathematics, fudan university,{2., china) fudan Univ Dept Math Shanghai 200433 Peoples R China

This paper extendes the results by E.M. Kasenally([7]) on a Generalized Minimum Backward Error Algorithm for nonsymmetric linear systems Ax = b to the problem in which pertubations are simultaneously permitted on A and b. The approach adopted by Kasenally has been to view the approximate solution as the exact solution to a perturbed linear system in which changes are permitted to the matrix A only. The new method introduced in this paper is a Krylov subspace iterative method which minimizes the norm of the perturbations to both the observation vector b and the data matrix A and has better performance than the Kasenally's method and the restarted GMRES method([12.). The minimization problem amounts to computing the smallest singular value and the corresponding right singular vector of a low-order upper-Hessenberg matrix. Theoratical properties of the algorithm are discussed and practical implementation issues are considered. The numerical examples are also given.

关键词： nonsymmetric linear systems iterative methods backward error

THE CODIMENSION FORMULA ON AF-COSUBMODULES

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Chinese Annals of mathematics,Series B 2002年第3期23卷 419-424页

作者： GUO KUNYU Department of mathematics, fudan university,{2., china Department of mathematics Fudan University Shanghai 200433 China

Let M1, M2.be submodules of analytic Hilbert module X on ?(? Cn) such that M1 ? M2.and dimM1/M2.= k < '. If M2.is an AF-cosubmodule, then the codimension dimM1/M2.of M2.in M1 equals the cardinality of zeros of M2.rel... 详细信息

Let M1, M2.be submodules of analytic Hilbert module X on ?(? Cn) such that M1 ? M2.and dimM1/M2.= k 2.is an AF-cosubmodule, then the codimension dimM1/M2.of M2.in M1 equals the cardinality of zeros of M2.related to MI by counting multiplicities. The codimension formula has some interesting applications. In particular, the author calculates out the dimension of Rudin quotient module, which is raised in [14].

关键词： AF-cosubmodule Characteristic space Analytic Hilbert module

FORMATION OF SINGULARITIES FOR A KIND OF QUASILINEAR NON-STRICTLY HYPERBOLIC SYSTEM

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Chinese Annals of mathematics,Series B 2002年第4期23卷 439-454页

作者： WANG LIBINInstitute of mathematics, fudan university,{2., china. Institute of mathematics Fudan University Shanghai 200433 China

The author gets a blow-up result of C1 solution to the Cauchy problem for a first order quasilinear non-strictly hyperbolic system in one space dimension.

关键词： Formation of singularity Quasilinear non-strictly hyperbolic system Weak linear degeneracy

BLOW UP OF SOLUTIONS TO THE CAUCHY PROBLEM FOR NONLINEAR WAVE EQUATIONS

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Chinese Annals of mathematics,Series B 2001年第3期22卷 275-280页

作者： ZHOU YI Institute of mathematics, fudan university,{2., china Institute of mathematics Fudan University Shanghai 200433 China

The author proves blow up of solutions to the Cauchy problem of certain nonlinear equations and, also, estimates the time when the blow up occurs.

关键词： Cauchy problem Nonlinear wave equation Blow up

ON A CONSTRUCTION OF INERTIALMANIFOLDS FOR A CLASS OF SECOND ORDER IN TIME EVOLUTION EQUATIONS

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Chinese Annals of mathematics,Series B 1999年第3期20卷 271-278页

作者： WANG ZONGXIN(Institute of mathematics, fudan university,{2., china.) fudan Univ Inst Math Shanghai 200433 Peoples R China

Inertial manifolds for a class of second order in time dissipative equations are *** author also proves an asymptotic completeness property for the inertial manifolds and characterizes the inertial manifolds as the set of trajectories whose growth is at most of order O(e-μt ) for some p > 0. As applications, a nonlinear wave equation and a problem of nonlinear oscillations of a shallow shell are considered.

关键词： Dynamical systems Inertial manifolds Nonlinear evolution equations

A NONLOCAL NONLINEAR BOUNDARYVALUE PROBLEM FOR THE HEAT EQUATIONS

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Chinese Annals of mathematics,Series B 1996年第3期17卷 365-374页

作者： YAN JINHAI(Department of mathematics, fudan university,{2., china) fudan UNIV DEPT MATHSHANGHAI 200433PEOPLES R CHINA

The existence and limit behaviour of the solution for a kind of nonlocal nonlinear boundaryvalue condition on a part of the boundary is studied for the heat equation, which physicallymeans that the potential is the function of the total flux. When this part of boundary shrinksto a point in a certain wayt this condition either results in a Dirac measure or simply disappearsin the corresponding problem.

关键词： Heat equation Nonlinear boundary problem Potential Limit behavior