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Hyperbolic positive mass theorem under modified energy condition

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Science china mathematics 2008年第12期51卷 2189-2197页

作者： xie naqing institute of mathematics, school of mathematical sciences,{2., Shanghai 2.0433, china institute of mathematics School of Mathematical Sciences Fudan University Shanghai 200433 China

We provide two new positive mass theorems under respective modified energy conditions allowing T00 negative on some compact set for certain modified asymptotically hyperbolic manifolds. This work is analogous to Zhang... 详细信息

关键词： positive mass theorem modified energy condition modified asymptotically hyperbolic 83C40 53C2.

RADIAL BASIS FUNCTION INTERPOLATION IN SOBOLEV SPACES AND ITS APPLICATIONS

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Journal of Computational mathematics 2007年第2期25卷 201-210页

作者： Manping Zhang (school of mathematical {2.,fudan university,Shanghai 2.0433,china institute of Computational mathematics,Chinese Academy of {2.,Beijing 100080,china school of mathematical {2. Fudan University Shanghai 200433 China institute of Computational mathematics Chinese Academy of Sciences Beijing 100080 China

In this paper we study the method of interpolation by radial basis functions and give some error estimates in Sobolev space H^k（Ω）（k 〉 1）. With a special kind of radial basis function, we construct a basis in H^k（Ω） and derive a meshless method for solving elliptic partial differential equations. We also propose a method for computing the global data density.

关键词： Sobolev space Radial basis function Global data density Meshless method

Riemann boundary value problems and reflection of shock for the Chaplygin gas

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Science china mathematics 2012年第4期55卷 671-685页

作者： CHEN ShuXing 1,& QU AiFang 2.1 school of mathematical sciences,fudan {2.,Shanghai 2.0433,china 2.Wuhan institute of Physics and mathematics,Chinese Academy of sciences,Wuhan 430071,china 1. school of mathematical sciences Fudan University Shanghai 200433 China2. Wuhan Institute of Physics and Mathematics Chinese Academy of Sciences Wuhan 430071 China

In this paper,we study two-dimensional Riemann boundary value problems of Euler system for the isentropic and irrotational Chaplygin gas with initial data being two constant states given in two sectors respectively,where one sector is a quadrant and the other one has an acute vertex *** prove that the Riemann boundary value problem admits a global self-similar solution,if either the initial states are close,or the smaller sector is also near a *** result can be applied to solving the problem of shock reflection by a ramp.

关键词： Riemann boundary value problem reflection of shock Chaplygin gas wave interaction Eulersystem

A maximum principle for optimal control problem of fully coupled forward-backward stochastic systems with partial information

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Science china mathematics 2009年第7期52卷 1579-1588页

作者： MENG QingXin1,2.1 Department of mathematical sciences,Huzhou {2.,Zhejiang 313000,china 2.institute of mathematics,fudan {2.,Shanghai 2.0433,china 1. Department of mathematical sciences Huzhou University Zhejiang 313000 China 2. institute of mathematics Fudan University Shanghai 200433 China

The paper is concerned with a stochastic optimal control problem in which the controlled system is described by a fully coupled nonlinear forward-backward stochastic differential equation driven by a Brownian *** is required that all admissible control processes are adapted to a given subfiltration of the filtration generated by the underlying Brownian *** this type of partial information control,one sufficient(a verification theorem) and one necessary conditions of optimality are *** control domain need to be convex and the forward diffusion coefficient of the system can contain the control variable.

关键词： maximum principle stochastic optimal control partial information 93E2. 60H10 60H30

GEOMETRIC INEQUALITIES FOR CERTAIN SUBMANIFOLDS IN A PINCHED RIEMANNIAN MANIFOLD

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Acta Mathematica Scientia 2007年第3期27卷 611-618页

作者：谢纳庆许洪伟 institute of mathematics Fudan University Center of mathematical sciences Zhejiang University

This article gives some geometric inequalities for a submanifold with parallel second fundamental form in a pinched Riemannian manifold and the distribution for the square norm of its second fundamental form.

关键词： Submanifolds second fundamental form pinched Riemannian manifold

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 {2. of Mining and Technology, Xuzhou 2.1008, china institute of mathematics, fudan university, Shanghai 2.0433, china school of mathematics and System sciences, Shandong {2., Jinan 2.0100, 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 {2. 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.

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 university, Shanghai 2.02.4,{2. 2. Laboratory of mathematics for Nonlinear sciences and institute of mathematics, fudan university, Shanghai 2.0433,{2. Department of mathematics Shanghai Normal University Shanghai China Laboratory of mathematics for Nonlinear sciences and {2. 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,{2., Shanghai 2.0433, 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,{2. Shanghai 2.0433, 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