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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, shanghai 200433, 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

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

Injective envelopes,cogenerators and direct products in the Doi-Hopf module category

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Chinese Science Bulletin 1999年第15期44卷 1350-1356页

作者： KAN HaibinInstitute of Mathematics , Fudau University, shanghai 200433, China Institute of Mathematics Fudau University Shanghai China

It is proved that there exist injective envelopes, cogenerators and direct products in the Doi-Hopf module category.

关键词： Doi-Hopf module injective envelope cogenerator.

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

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.

Averaging of Hamilton-Jacobi equation in infinite dimensions and application

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Chinese Science Bulletin 1998年第1期43卷 30-32页

作者： WANG Shihong Institute of Mathematics, Fudan University, shanghai 200433, China Fudan University Institute of Mathematics Shanghai China

The averaging of Hamilton_Jacobi equation with fast variables in viscosity solution sense in infinite dimensions is studied. It is proved that viscosity solution of the original equation converges to viscosity solution of the averaged equation and this result is applied to study the limit problem of the value function for optimal control problem with fast variables.

关键词： infinite dimensions averaging of HJB equation viscosity solution optimal control problem value function.

ON INTERACTION OF SHOCK AND SOUND WAVE (Ⅰ)

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Chinese Annals of Mathematics,Series B 1996年第4期17卷 35-42页

作者： CHEN SHUXING(Institute of Mathematics, Fudan University shanghai 200433, China.) 复旦大学数学系上海

This paper studies the ioteraction of shock and gradient wave (sound wave) of solutions to the system of inviscid isentropic gas dynamics as a model for the corresponding problems for nonlinear hyperbolic systems. The problem can be reduced to a boundary value problem in a wedged domain. By using the method of constructing asymptotic solutions and Newton’s iteration process it is proved that if a weak shock hits a gradient wave, then the grandient wave will split into two gradient waves, while the shock continuses propagating. In this paper the author reduces the problem to a standard form and constructs asymptotic solution of the problem. The existence of the genuine solution will be given in the following paper.

关键词： Shock wave Sound wave Nonliner hyperbolic system Asymptotic solution

GROUP ACTIONS ON VON NEUMANN REGULAR RINGS

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Chinese Annals of Mathematics,Series B 1994年第2期15卷 235-240页

作者： ZHANG YINHUO(Institute of Mathematics,Fudan University, shanghai 200433, China) FUDAN UNIV INST MATHSHANGHAI 200433PEOPLES R CHINA

Let A be a ring with indentity, G a finite group of automorphisms of A. The main result of this paper is that A/AG is Galois if and only if it is Frobenius and the module AGA (or AAG)is faithful. Moreover if |G| is in... 详细信息

关键词： Von Neumann regular ring Extension Group Automorphism.

PIXE and INAA studies on ancient potteries from Guangfulin relics in shanghai

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Progress in Natural Science:Materials International 2007年第11期17卷 1348-1356页

作者： Lin Jiawei1, Cheng Huansheng1, Zhang Zhengquan1, Zhang Bin1, Feng Songlin2, Song Jian3, Gao Menghe4 and Zhu Dan1(1. Applied Ion Beam Physics Laboratory, Key Laboratory of the Ministry of Education, Institute of Modern Physics, Fudan University, shanghai 200433, China 2. Key Laboratory of Nuclear Analytical Techniques, Institute of High Energy Physics, Beijing 100039, China 3. shanghai Museum, shanghai 200003, China 4. Department of Cultural Heritage and Museology, Fudan University, shanghai 200433, China) Applied Ion Beam Physics Laboratory Key Laboratory of the Ministry of Education Institute of Modern Physics Fudan University Shanghai 200433 China Key Laboratory of Nuclear Analytical Techniques Institute of High Energy Physics Beijing 100039 China shanghai Museum Shanghai 200003 China Department of Cultural Heritage and Museology Fudan University Shanghai 200433 China

This paper reports the study of ancient potteries unearthed from the Guangfulin site in shanghai. From the external features of these potteries, archeologists can classify them into two different cultural types: Liangzhu culture (local culture) and a new culture which might be derived elsewhere, but they can not recognize whether they were produced in the same place. Proton induced X-ray emission (PIXE) and instrumental neutron activation analysis (INAA) were used to measure the chemical compositions of the samples and the results were analyzed using multivariate statistics. We found that the two methods can complement each other and their database can be mutually referenced in the study of ancient potteries. Experimental results show that the compositions of the potteries from the two cultural types are different, which means that the materials for ancient potteries of new culture originate from elsewhere. This supports the archaeologists’ speculation that a group of ancient people migrated to shanghai from some other places 4000 years ago.

关键词： PIXE INAA factor analysis Guangfulin ancient pottery