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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, Shanghai 200433, 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 Shanghai 200433, 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, Shanghai 200433, 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

Modern thermodynamics-New concepts based on the second law of thermodynamics

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Progress in Natural Science:Materials International 2009年第1期19卷 125-135页

作者： Jitao Wang Department of Microelectronics,fudan university,Shanghai 200433,China [a]Department of Microelectronics Fudan University Shanghai 200433 China

Thermodynamics is a core part of *** all scientists should have a basic knowledge of *** is a science of development,and is a viewpoint of scientific development in natural *** of thermodynamics has influence not only on natural sciences,but also on social sciences and *** concepts and definitions are very important for any discipline of science,so what is classical thermodynamics and what is modern thermodynamics have become the key points of puzzledom in *** this paper,after clarification of fundamental concept in thermodynamics,a complete basic modern classification of thermodynamics is naturally *** is suggested that extended Carnot theorem and dissipation decrease theorem,together with the laws of thermodynamics,are the most fundamental theorems in thermodynamics *** thermodynamics is a new field besides equilibrium thermodynamics belonging to the equal part of the second law of thermodynamics.

关键词： Modern thermodynamics Second law of thermodynamics Thermodynamic coupling Spiral reactions Chemical oscillation Low-pressure diamond growth

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, Shanghai 200433, 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, Shanghai 200433, 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

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, Shanghai 200433, 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 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

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, Shanghai 200433, 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

The neural mechanisms of pain-related affect and memory

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Progress in Natural Science:Materials International 2006年第4期16卷 338-345页

作者： ZHANG Yuqiu Institute of Neurobiology, fudan university, Shanghai 200433, China [a]Institute of Neurobiology Fudan University Shanghai China

The pain experience includes a sensory-discriminative and an emotional-affective components. The affective dimension refers to the unpleasantness or aversion of sensation. The great progress at the genetic, molecular, cellular, and systemic levels on the study of the sensory dimension of pain has been made over past four decades. However, "to consider only the sensory features of pain, and ignore its motivational and affective properties, is to look at only part of the problem and not even the most important part of that". A line of clinic observations indicate that the patients with chronic pain suffer from much more affective disturbance than pain itself. Obviously, physiological arousal and hypervigilance to pain cause negative affect, such as anxiety, anger, worry, aversion, even tendency of suicide, these negative affective states in turn enhance pain sensation. Today, more and more attention has been paid to the study on mechanisms underlying affective dimension of pain. In order to deepen and expand our understanding of the nature of pain, this review summarizes the main progress and recent findings from our laboratory regarding affective component of pain in neuroanatomy, neurophysiology, and cell biochemistry.

关键词： pain emotion medial pain system anterior cingnlate cortex formalin conditioned place avoidance cAMP responsive element binding protein extracellular signal-regulated kinase.