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Global Exact Boundary Controllability for Cubic Semi-linear Wave Equations and Klein-Gordon Equations

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Chinese Annals of Mathematics,Series B 2010年第1期31卷 35-58页

作者： Yi ZHOU Wei XU Zhen LEI Key Laboratory of Mathematics for Nonlinear sciences School of Mathematical Sciences Fudan University Shanghai 200433 China school of Mathematical sciences Fudan University Shanghai 200433 China

The authors prove the global exact boundary controllability for the cubic semilinear wave equation in three space dimensions,subject to Dirichlet,Neumann,or any other kind of boundary controls which result in the well-posedness of the corresponding initial-boundary value *** exponential decay of energy is first established for the cubic semi-linear wave equation with some boundary condition by the multiplier method,which reduces the global exact boundary controllability problem to a local *** proof is carried out in line with [2,15].Then a constructive method that has been developed in [13] is used to study the local *** when the region is star-complemented,it is obtained that the control function only need to be applied on a relatively open subset of the *** the cubic Klein-Gordon equation,similar results of the global exact boundary controllability are proved by such an idea.

关键词： Global exact boundary controllability Cubic semi-linear wave equations The exponential decay Star-shaped Star-complemented Cubic Klein- Gordon equations

THE CAPACITY DENSITY AND THE HAUSDORFF DIMENSION OF FRACTAL SETS

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Chinese Annals of Mathematics,Series B 1995年第1期16卷 43-50页

作者： Xu You (Institute of Mathematics, fudan university, shanghai 200433, shanghai, china). fudan UNIV INST MATHSHANGHAI 200433PEOPLES R CHINA

This paper defines the upper capacity densities of the subsets of R￣n, gets uniform lower bound of the upper capacity densities for -almost all points of the Hausdorff s-sets or the analytic sets with Hausdorff dimen... 详细信息

关键词： Capacity density Hausdorff dimension Fractal set.

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

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.

Limit theorem and uniqueness theorem of backward stochastic differential equations

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Science china Mathematics 2006年第10期49卷 1353-1362页

作者： JIANG Long Department of Mathematics, china university of Mining and Technology, Xuzhou 221008, china Institute of Mathematics, fudan university, shanghai 200433, china school of Mathematics and System sciences, Shandong university, Jinan 250100, china 1. Department of Mathematics China University of Mining and Technology Xuzhou 221008 China 2. Institute of Mathematics Fudan University Shanghai 200433 China 3. school of Mathematics and System sciences Shandong University Jinan 250100 China

This paper establishes a limit theorem for solutions of backward stochastic differential equations (BSDEs). By this limit theorem, this paper proves that, under the standard assumption g(t,y,0) = 0, the generator g of a BSDE can be uniquely determined by the corresponding g-expectationεg;this paper also proves that if a filtration consistent expectation S can be represented as a g-expectationεg, then the corresponding generator g must be unique.

关键词： backward stochastic differential equation, g-expectation, generator.

Recent developments of nanoparticle-based enrichment methods for mass spectrometric analysis in proteomics

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Science china Chemistry 2010年第4期53卷 695-703页

作者： ZHANG LiJuan, LU HaoJie & YANG PengYuan Department of Chemistry and Institutes of Biomedical sciences, fudan university, shanghai 200433, china 1. Department of Chemistry and Institutes of Biomedical sciences Fudan University Shanghai 200433 China

In proteome research, rapid and effective separation strategies are essential for successful protein identification due to the broad dynamic range of proteins in biological samples. Some important proteins are often expressed in ultra low abundance, thus making the pre-concentration procedure before mass spectrometric analysis prerequisite. The main purpose of enrichment is to isolate target molecules from complex mixtures to reduce sample complexity and facilitate the subsequent analyzing steps. The introduction of nanoparticles into this field has accelerated the development of enrichment methods. In this review, we mainly focus on recent developments of using different nanomaterials for pre-concentration of low-abundance peptides/ proteins, including those containing post-translational modifications, such as phosphorylation and glycosylation, prior to mass spectrometric analysis.

关键词： enrichment nanoparticles mass spectrometry proteomics phosphorylation glycosylation

CLASSIFICATION OF AF-ALGEBRAS AND THEIR DIMENSION GROUPS

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Chinese Annals of Mathematics,Series B 1994年第2期15卷 181-192页

作者： HUANG ZHAOBO(Institute of Mathematics, fudan university, shanghai 200433, shanghai, china) fudan UNIV INST MATHSHANGHAI 200433PEOPLES R CHINA

This paper gives the intrinsic character of the classification for AF-algebras defined by *** and G. K. Pedersen in terms of their dimension groups.

关键词： AF-algebra Demension group Classification.

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.

Optimal variational principle for backward stochastic control systems associated with Lévy processes

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Science china Mathematics 2012年第4期55卷 745-761页

作者： TANG MaoNing 1 & ZHANG Qi 2,1 Department of Mathematical sciences,Huzhou university,Huzhou 313000,china 2 school of Mathematical sciences,fudan university,shanghai 200433,china 1. Department of Mathematical sciences Huzhou University Huzhou 313000 China2. School of Mathematical Sciences Fudan University Shanghai 200433 China

The paper is concerned with optimal control of backward stochastic differentiM equation （BSDE） driven by Teugel＇s martingales and an independent multi-dimensional Brownian motion, where Teugel＇s martingales are a family of pairwise strongly orthonormal martingales associated with L6vy processes （see e.g., Nualart and Schoutens＇ paper in 2000）. We derive the necessary and sufficient conditions for the existence of the optimal control by means of convex variation methods and duality techniques. As an application, the optimal control problem of linear backward stochastic differential equation with a quadratic cost criteria （or backward linear-quadratic problem, or BLQ problem for short） is discussed and characterized by a stochastic Hamilton system.

关键词： stochastic control stochastic maximum principle Ldvy processes Teugel's martingales backwardstochastic differential equations